Lyubomir T. Gruyitch
The human has been developing automatic control in order to satisfy three natural imperatives (three instincts): the instinct of selfpreservation, the species preservation  the sexual instinct, and, in my opinion, the game instinct (the game in its widest sense that incorporates art) with the best quality, minimal efforts and spending less time. I have devoted my teaching and research continuously to dynamical systems and systems control; last two decades also to TIME properties, relativity.
Biography
HONORSFrench Republic honored Professor Gruyitch Doctor Honoris Causa of the University of Lille I, for scientific and educational contributions to Systems Science and Control Theory (1984).
Association of Serbia for Systems, Automatic Control and Measurement honored Professor Gruyitch Distinguished and Honorary Member (1989).
The highest honor by the Faculty of Mechanical Engineering (FME), University of Belgrade, Serbia, 1997.
AWARDS
City of Belgrade and the First Belgrade High School (1958), Belgrade University (1960), and Slovenian industry "Iskra" (1971) honored Mr. Gruyitch with their prestigious academic awards.
EDUCATION
Mr. Lyubomir T. Gruyitch is Certified Mechanical Engineer (Dipl. M. Eng.), Master of Electrical Engineering Sciences (M. E. E. Sc.), and Doctor of Engineering Sciences (D. Sc.) (All with the University of Belgrade, Serbia).
RESEARCH
The main scientific and engineering contributions and interests by Dr. Lyubomir T. Gruyitch have been in the next areas:
Â° Dynamics and modeling of engineering systems including neural and fuzzyneural networks.
Â° Linear and nonlinear control systems theory. Synthesis of robust, stabilizing and/or tracking control of technical plants.
Â° Stability theory of nonlinear dynamical systems with diverse applications.
Â° Time, physical principles, relativity theory, dynamical systems with multiple time scales and control.
Â° Trackability and tracking theory of linear and nonlinear control systems. Its applications to various technical plants.
Dr. Gruyitch was a leading contributor to the creation of the research Laboratory of Automatic Control, Mechatronics, Manufacturing Engineering and Systems Engineering of the National School of Engineers (Belfort, France), and a founder of the educational and research Laboratory of Automatic Control of the FME.
EMPLOYMENT (*with tenure): TEACHING AND RESEARCH
France * (retired May 1, 2007), South Africa (10 years contract), France (visiting), United States of America (visiting), Serbia *.
PUBLICATIONS
Dr. Gruyitch published 8 books, 4 textbooks, 11 lecture notes (in English, French or Serb), one manual of solved problems, one book translation from Russian, chapters in eight scientific books, 127 scientific papers in scientific journals, 170 conference research papers and two educational papers.
SUPERVISOR OF THESES
Professor Gruyitch supervised one doctorate at the University of Technology BelfortMontbeliard  UTBM (France), which gained the highest grade by an international (French  USA) jury, five doctorates at the University of Belgrade (Serbia), four DEA (equivalent to M. Sc.) theses at the ENI and five master theses at the University of Belgrade.
CONTRIBUTIONS TO EDUCATION
Professor Gruyitch was a coinitiator of the proposal for a new tentative, highly advanced, Department of Automatique et SystĂ©mique at the UTBM, and the Coordinator of the team that worked out the full project. He was cofounder of the Cathedra of Automatic Control and of the undergraduate and graduate Group of Automatic Control of the FME. He introduced a number of new courses at the universities in France, South Africa and Serbia.
INDUSTRIAL COOPERATION
Professor Gruyitch was the principal investigator supervising several projects funded by industry in Serbia.
ADMINISTRATIVE, EDUCATIONAL AND LEADERSHIP RESPONSIBILITIES
Professor Gruyitch was a member of the Acting Senate of the UTBM and the Coordinator of the Commission of Research of the UTBM. He was the Chief of the Cathedra of Automatic Control, the Chief of the Laboratory of Automatic Control and the President of the Senate of the Faculty of Mechanical Engineering, Belgrade.
INVITED UNIVERSITY SEMINARS and INTERNATIONAL SCIENTIFIC CONFERENCES
Dr. Gruyitch gave invited university seminars in Belgium, Canada, England, France, Russia, Serbia, Tunis and USA.
Professor Gruyitch was invited plenary sessions speaker, Organizer and/or Chairman of invited sessions at the international conferences, and President of the International Program Committee of the IFAC  IFIP  IMACS Conference Control of Industrial Systems, Belfort, France (more than 300 participants from 42 countries with four continents).
For more details see: http://www.truthscience.info
Education

Diplomed (Certified) Mechanical Engineer, Faculty of Mechanical Engineering, University of Belgrade, 1963. M. Sci., Faculty of Electrical Engineering, University of Belgrade, 1971, D. Sci., Faculty of Mechanical Engineering, University of Belgrade, 1972
Areas of Research / Professional Expertise

Dynamics and modelling of mechanical and thermal plants.
Stability of dynamic systems including large scale dynamic systems, and singularly perturbed dynamic systems. Stabilizing control synthesis.
Neural and fuzzyneural networks.
Tracking, trackability and tracking control synthesis.
Time, its consistent relativity theory and links with physical variables, dynamical systems and control.
Personal Interests

Social and academic life, state and society control, sports, art.
Books
Photos
News
Trackability and Tracking of General Linear Systems
By: Lyubomir T. Gruyitch
Subjects: Engineering  Chemical, Engineering  Electrical, Engineering  General, Engineering  Mechanical, Mathematics, Physics
Trackability and Tracking of General Linear Systems
1st Edition
Lyubomir T. Gruyitch
CRC Press
November 2, 2018
Reference  378 Pages  13 B/W
Illustrations
ISBN 9781138353374  CAT# K395516
Summary
Trackability and Tracking of General Linear Systems deals with five classes of the systems, three of which are new, begins with the definition of time together with a brief description of its crucial properties and with the principles of the physical uniqueness and continuity of physical variables. They are essential for the natural tracking control synthesis. The book presents further new results on the new compact, simple and elegant calculus that enabled the generalization of the transfer function matrix concept and of the state concept, the completion of the trackability and tracking concepts together with the proofs of the trackability and tracking criteria, as well as the natural tracking control synthesis for all five classes of the systems.
Features
• Crucially broadens the state space concept and the complex domain fundamentals of the dynamical systems to the control systems.
• Addresses the knowledge and ability necessary to study and design control systems that will satisfy the fundamental control goal.
• Outlines new effective mathematical means for effective complete analysis and synthesis of the control systems.
• Upgrades, completes and essentially generalizes the control theory beyond the existing boundaries.
• Provides information necessary to create and teach advanced inherently upgraded control courses.
Observability and Controllability of General Linear Systems
By: Lyubomir T. Gruyitch
Subjects: Engineering  Chemical, Engineering  Electrical, Engineering  General, Engineering  Mechanical, Mathematics, Physics
Observability and Controllability of General Linear Systems
1st Edition
Lyubomir T. Gruyitch
CRC Press
November 2, 2018
Reference  335 Pages  1 B/W Illustrations
ISBN 9781138353152  CAT# K395488
Summary
Observability and Controllability of General Linear Systems treats five different families of the linear systems, three of which are new. The book begins with the definition of time together with a brief description of its crucial properties. It presents further new results on matrices, on polynomial matrices, on matrix polynomials, on rational matrices, and on the new compact, simple and elegant calculus that enabled the generalization of the transfer function matrix concept and of the state concept, the proofs of the new necessary and sufficient observability and controllability conditions for all five classes of the studied systems.
Features
• Generalizes the state space concept and the complex domain fundamentals of the control systems unknown in previously published books by other authors.
• Addresses the knowledge and ability necessary to overcome the crucial lacunae of the existing control theory and drawbacks of its applications.
• Outlines new effective mathematical means for effective complete analysis and synthesis of the control systems.
• Upgrades, completes and broadens the control theory related to the classical selfcontained control concepts: observability and controllability.
• Provides information necessary to create and teach advanced inherently upgraded control courses.
Linear DiscreteTime Systems
By: Lyubomir T. Gruyitch
Subjects: Engineering  Chemical, Engineering  Electrical, Engineering  Mechanical, Mathematics
Linear DiscreteTime Systems
Zoran M. Buchevats, Lyubomir T. Gruyitch
November 8, 2017 by CRC Press
Reference  454 Pages
ISBN 9781138039599  CAT# K32971
https://www.crcpress.com/LinearDiscreteTimeSystems/BuchevatsGruyitch/p/book/9781138039599
Features
 Discovers the existence of the system full transfer function matrix F(z) and defines and determines it for IO, ISO, and IIO systems.
 Establishes the full block diagram technique and the full system matrix P(z), both based on the use of F(z).
 Introduces new dynamical system and control tools, which are not available in existing texts.
 Explores the concept and definition of the IO systems and IIO systems state, and uses it in the stability study.
Summary
This book covers crucial lacunae of the linear discretetime timeinvariant dynamical systems and introduces the reader to their treatment, while functioning under real, natural conditions, in forced regimes with arbitrary initial conditions. It provides novel theoretical tools necessary for the analysis and design of the systems operating in stated conditions. The text completely covers two wellknown systems, IO and ISO, along with a new system, IIO. It discovers the concept of the full transfer function matrix F(z) in the zcomplex domain, which incorporates the Ztransform of the system, input and another variable, vectors, all with arbitrary initial conditions. Consequently, it addresses the full system matrix P(z) and the full block diagram technique based on the use of F(z), which incorporates the Ztransform of the system, input and another variable, vectors, all with arbitrary initial conditions. The book explores the direct relationship between the system full transfer function matrix F(z) and the Lyapunov stability concept, definitions, and conditions, as well as with the BI stability concept, definitions, and conditions. The goal of the book is to unify the study and applications of all three classes of the linear discretetime timeinvariant system, for short systems.
Linear ContinuousTime Systems
By: Lyubomir T. Gruyitch
Subjects: Engineering  Chemical, Engineering  Electrical, Engineering  General, Engineering  Mechanical, Mathematics
Linear ContinuousTime Systems
Lyubomir T. Gruyitch
Features
 Discovers the existence of the system full transfer function matrix F(s) and defines and determines it for IO, ISO and IIO systems (the new class of the systems introduced in the book).
 Establishes the full block diagram technique and the full system matrix P(s) both based on the use of F(s).
 Introduces new dynamical system and control tools, which are not available in existing texts.
 Explores the concept and definition of the IO systems and of the IIO systems state and uses it in the stability study.
 Provides the understanding, knowledge, and capability to analyze and design all three classes of the systems.
Summary
This book aims to help the reader understand the linear continuoustime timeinvariant dynamical systems theory and its importance for systems analysis and design of the systems operating in real conditions, i.e., in forced regimes under arbitrary initial conditions. The text completely covers IO, ISO and IIO systems. It introduces the concept of the system full matrix P(s) in the complex domain and establishes its link with the also newly introduced system full transfer function matrix F(s). The text establishes the full block diagram technique based on the use of F(s), which incorporates the Laplace transform of the input vector and the vector of all initial conditions. It explores the direct relationship between the system full transfer function matrix F(s) and the Lyapunov stability concept, definitions and conditions, as well as with the BI stability concept, definitions, and conditions. The goal of the book is to unify the study and applications of all three classes of the of the linear continuoustime timeinvariant systems, for short systems.
Nonlinear Systems Tracking
By: Lyubomir T. Gruyitch
Subjects: Engineering  Chemical, Engineering  Electrical, Engineering  General, Engineering  Mechanical, Mathematics
Nonlinear Systems Tracking
Lyubomir T. Gruyitch
January 2, 2016 by CRC Press
Reference  478 Pages  16 B/W
Illustrations
ISBN 9781498753258  CAT#
K27341
Features
 Covers a very large class of timevarying nonlinear systems that incorporate the anyorder inputoutput systems and those determined by the classical statespace description
 Presents new theories and concepts that begin by defining new system and control properties and end with the criteria or with the conditions on the system
 Solves the problem of achieving the tracking control task whatever the physical (biological, chemical, economical, electrical, electromechanical, mechanical, or social) nature of the plant
 Addresses the dynamical and control problems caused by the complexity of the system
 Uses the new simple vector and matrix notation analogous to the scalar notation
Summary
Tracking is the goal of control of any object, plant, process, or vehicle. From vehicles and missiles to power plants, tracking is essential to guarantee highquality behavior.
Nonlinear Systems Tracking establishes the tracking theory, trackability theory, and tracking control synthesis for timevarying nonlinear plants and their control systems as parts of control theory. Treating general dynamical and control systems, including subclasses of inputoutput and statespace nonlinear systems, the book:
 Describes the crucial tracking control concepts that comprise effective tracking control algorithms
 Defines the main tracking and trackability properties involved, identifying properties both perfect and imperfect
 Details the corresponding conditions needed for the controlled plant to exhibit each property
 Discusses various algorithms for tracking control synthesis, attacking the tracking control synthesis problems themselves
 Depicts the effective synthesis of the tracking control, under the action of which, the plant behavior satisfies all the imposed tracking requirements resulting from its purpose
With clarity and precision, Nonlinear Systems Tracking provides original coverage, presenting discovery and proofs of new tracking criteria and control algorithms. Thus, the book creates new directions for research in control theory, enabling fruitful new control engineering applications.
New avenue in control theory and engineering: NONLINEAR SYSTEMS TRACKING
By: Lyubomir T. Gruyitch
Subjects: Engineering  Chemical, Engineering  Electrical, Engineering  General, Engineering  Mechanical, Mathematics
Nonlinear Systems Tracking
Lyubomir T. Gruyitch
January 2, 2016 by CRC Press
Reference  478 Pages  16 B/W Illustrations
ISBN 9781498753258  CAT# K27341
https://www.crcpress.com/NonlinearSystemsTracking/Gruyitch/9781498753258
Features
 Covers a very large class of timevarying nonlinear systems that incorporate the anyorder inputoutput systems and those determined by the classical statespace description
 Presents new theories and concepts that begin by defining new system and control properties and end with the criteria or with the conditions on the system
 Solves the problem of achieving the tracking control task whatever the physical (biological, chemical, economical, electrical, electromechanical, mechanical, or social) nature of the plant
 Addresses the dynamical and control problems caused by the complexity of the system
 Uses the new simple vector and matrix notation analogous to the scalar notation
Summary
Tracking is the goal of control of any object, plant, process, or vehicle. From vehicles and missiles to power plants, tracking is essential to guarantee highquality behavior.
Nonlinear Systems Tracking establishes the tracking theory, trackability theory, and tracking control synthesis for timevarying nonlinear plants and their control systems as parts of control theory. Treating general dynamical and control systems, including subclasses of inputoutput and statespace nonlinear systems, the book:
 Describes the crucial tracking control concepts that comprise effective tracking control algorithms
 Defines the main tracking and trackability properties involved, identifying properties both perfect and imperfect
 Details the corresponding conditions needed for the controlled plant to exhibit each property
 Discusses various algorithms for tracking control synthesis, attacking the tracking control synthesis problems themselves
 Depicts the effective synthesis of the tracking control, under the action of which, the plant behavior satisfies all the imposed tracking requirements resulting from its purpose
With clarity and precision, Nonlinear Systems Tracking provides original coverage, presenting discovery and proofs of new tracking criteria and control algorithms. Thus, the book creates new directions for research in control theory, enabling fruitful new control engineering applications.
GALILEANâ€“NEWTONEAN REBUTTAL TO EINSTEINâ€™S RELATIVITY THEORY
By: Lyubomir T. Gruyitch
Subjects: Engineering  Electrical, Engineering  Mechanical, Mathematics, Physics
GALILEAN–NEWTONEAN REBUTTAL TO
EINSTEIN’S RELATIVITY
THEORY
Lyubomir T. Gruyitch, Serbia
ISBN13: 9781907343414; 390 pages, hardback, February 2015; £80.00/$125.00
http://www.cisppublishing.com/acatalog/info_124.html
GalileanNewtonean physics is the basis for the presented indebt study of Einstein`s works. Rigorous, exact, proofs of the EINSTEIN’S RELATIVITY full physical failure and mathematical sever restrictions on the validity of Einstein`s formulae exclusively under Einstein`s physically meaningless and mathematically unjustifiable assumptions The book discovers a number of the inconsistences, mistakes and paradoxes of Einstein`s relativity theory. The book presents the proofs that Einstein`s claims (lifted to the level of uncontested postulates) on the relativity of time itself, on the existence of several times and the time speeds, on the time dependence on space (frames), on the invariance of the light speed are wrong and physically meaningless. The book discovers Einstein`s tacit assumptions accepted a priory, which form the basis for all his mathematical results. The book explains and shows that all the assumptions are inacceptable, which makes all his mathematical results formally valid only under such assumptions and that his theory represents from the formal mathematical view point exclusively a singular case.
Order on line at: www.cisppublishing.com/acatalog/info_124.html
New, consistent, time relativity theory: TIME AND CONSISTENT RELATIVITY
By: Lyubomir T. Gruyitch
Subjects: Engineering  Electrical, Engineering  General, Engineering  Mechanical, Mathematics, Physics
Time and Consistent Relativity
Physical and Mathematical Fundamentals
Lyubomir T. Gruyitch, DSc
http://www.appleacademicpress.com/title.php?id=9781771881111
In
production
Pub
Date: April,
2015
Hardback
Price: $179.95
US  £114.00
Hard
ISBN: 9781771881111
Pages: Approx
599pp+index
Binding
Type: hardback
Time and Consistent
Relativity: Physical and Mathematical
Fundamentals establishes a new and original theory of time
relativity, which is fully consistent. It explains why Einstein`s
theory of time relativity is physically meaningless and
mathematically based on tacit inacceptable assumptions, and why it
represents the singular case from the mathematical point of view.
The consistent relativity theory established in the book represents
an exit from the situation created by Einstein`s theory of time
relativity.
This original book presents novel results on time and its
relativity that constitute the consistent relativity theory. The
results are free of mistakes, inconsistencies, and paradoxes of
Einstein`s time relativity theory. The author’s original
discoveries and results constitute the new physical and
mathematical fundamentals on time and its relativity. The book
presentation is concise, clear, and selfcontained. It covers the
phenomenon of time and its properties and results in a definition
and characterization of time. It enables the great variety of new
mathematical results presented in the form of theorems and their
corollaries and specifies the necessary and sufficient conditions
for the corresponding statements to hold. The proofs are
rigorous.
This book:
 explains the physical nature of time
 presents the definition and characterization of time
 explains the physical sense of time relativity
 rejects Einstein’s time relativity theory as the general one
 proves that Einstein’s time relativity theory represents a singular case valid under tacit, physically meaningless and mathematically inacceptable, assumptions
 generalizes and extends the GalileanNewtonian meaning of time and its relativity
 introduces various new classes of mathematical transformations related to temporal, spatial, and velocity coordinates and proves the necessary and sufficient conditions for their validity
 discovers a great specter of new results on the time uniqueness, relativity, temporal speed
 discovers and proves a great specter of new results on the velocity and its transformations
 discovers and proves a great specter of new results on the light speed and its invariance and noninvariance
 discovers and proves the relationship of the light speed and the upper limiting speed
 opens new directions for further research in physics and mathematical physics.
CONTENTS:
Preface
Introduction
PART I. TIME
1. Interpretations of Time
1.1 Introductory comment
1.2 Time as a topic
1.3 Arts and time
1.4 Biology and time
1.5 Economics and time
1.6 Human and time
1.7 Information and time
1.8 Mathematics and time
1.9 Philosophy and time
1.10 Physics and time
1.11 Psychology and time
1.12 Religion and time
1.13 Works on time in general
1.14 Works on time
2. Newton and Einstein on Time
2.1 Newton's explanation of time
2.2 Einstein's interpretation of time
2.3 Einstein's versus Newton's explanation
3. Nature and Properties of Time
3.1 Quantities, dimensions and units
3.2 Definition and properties of time
3.3 Time scales, units and interval mappings
3.4 Physical variables and spaces
3.5 Physical constituents of the existence
3.6 Time, space and events. Simultaneity
3.7 Time, velocity and light velocity
3.8 Clock principles
3.9 Time and movement
3.10 Human and time
4. New Fundamentals
4.1 Physical variables, time and new principles
4.2 Modeling and relativity principles
4.3 Time, principles and dynamical systems
4.4 New fundamental theorems
PART II. TIME FIELDS AND RELATIVITY
5. Time Fields and Transformations
5.1 Time field: definition and properties
5.2 Time fields. Generic transformations
5.3 Compatibility. Consistency
5.4 Basic mathematical problem
5.5 General, special and singular case
6. Why not Einstein`s Relativity Theory?
6.1 Einstein's condition and transformations
6.2 Time Fields and Lorentz transformations
6.3 Failure of Einstein`s Relativity Theory
6.4 Inapplicability of Lorentz transformations
6.5 Paradoxes of Lorentz transformations
6.6 Einstein`s paradoxes, mistakes and absurd
6.7 Concluding rebuttals to Einstein`s postulates
6.8 Conclusion on Einstein's Theory
7. NonEinsteinean Approaches to Relativity
7.1 Galilean  Newtonean approach
7.2 Dynamical systems approach to relativity
7.3 Generalized Galilean  Newtonean approach
7.4 Guideline
8. Conclusion on Time and Time Fields
PART III. PARTIALLY COMPATIBLE BUT CONSISTENT (PCC)
RELATIVITY THEORY (RT)
9. Partial Compatibility
9.1 Origin of partial compatibility
9.2 Timeinvariant nonuniformity
9.3 Timeinvariant uniformity
10. Light Speed of the Arbitrary Point
10.1 General nonuniformity
10.2 Nonuniformity
10.3 Weak nonuniformity
10.4 Uniformity: general through special
10.5 Weak uniformity results
10.6 Relative uniformity results
11. Any Speed of the Arbitrary Point
11.1 General spatial uniformity
11.2 General complete uniformity
12. Conclusion on PCC Relativity Theory
PART IV. COMPATIBLE AND CONSISTENT (CC) RELATIVITY
THEORY
13. Colinear Motions: Transformations
13.1 Importance. Timeinvariance
13.2 Nonuniformity: general
13.3 Nonuniformity: ordinary
13.4 Nonuniformity: weak
13.5 General uniformity
13.6 Uniformity
13.7 Special uniformity
13.8 General weak uniformity
13.9 Weak uniformity
13.10 Special weak uniformity
13.11 General relative uniformity
13.12 Relative uniformity
13.13 Special relative uniformity
13.14 Conclusion on colinear motions
14. Noncolinear Motions: Transformations
14.1 Generic forms
14.2 General nonuniformity
14.3 General uniformity
14.4 General weak uniformity
14.5 General relative uniformity
14.6 Conclusion on noncolinear motions
15. Conclusion on CC Relativity Theory
PART V. GENERAL CONCLUSION
PART VI. SUBSIDIARY PARTS
16. Bibliography
17. Notational Details
18. Appendices: Proofs
19. Indexes
Tracking Control of Linear Systems
By: Lyubomir T. Gruyitch
Subjects: Engineering  Electrical, Engineering  Mechanical, Mathematics
Tracking Control of Linear Systems
CRC Press, Taylor & Francis Group, Boca Raton, FL, USA, 2013
ISBN: 9781466587519
http://www.crcpress.com/product/isbn/9781466587519
Features
 Introduces the full transfer function matrix, which is a crucial complex domain characteristic of linear dynamical and control systems that can be used under arbitrary inputs and initial conditions
 Establishes the new fundamentals of the complex domain theory of linear dynamic and control systems
 Shows how the full transfer function matrix enables you to synthesize control of linear systems to work more effectively in real environments
 Discusses tracking and trackability fundamentals and their significance for control synthesis
 Presents novel, sophisticated approaches and methods for tracking control design
 Includes theorem proofs in the appendices
Summary
The primary purpose of control is to force desired behavior in an unpredictable environment, under the actions of unknown, possibly unmeasurable disturbances and unpredictable, and therefore probably nonzero, initial conditions. This means that tracking and tracking control synthesis are fundamental control issues. Surprisingly, however, tracking theory has not been well developed, and stability theory has dominated. Tracking Control of Linear Systems presents the fundamentals of tracking theory for control systems. The book introduces the full transfer function matrix F(s), which substantially changes the theory of linear dynamical and control systems and enables a novel synthesis of tracking control that works more effectively in real environments.
An Introduction to the New Fundamentals of the Theory of Linear Control Systems
The book begins by reexamining classic linear control systems theory. It then defines and determines the system full (complete) transfer function matrix F(s) for two classes of systems: inputoutput (IO) control systems and inputstateoutput (ISO) control systems. The book also discusses the fundamentals of tracking and trackability. It presents new Lyapunov tracking control algorithms and natural tracking control (NTC) algorithms, which ensure the quality of the tracking under arbitrary disturbances and initial conditions. This natural tracking control is robust, adaptable, and simple to implement.
Advances in Linear Control Systems Theory: Tracking and Trackability
This book familiarizes readers with novel, sophisticated approaches and methods for tracking control design in real conditions. Contributing to the advancement of linear control systems theory, this work opens new directions for research in timeinvariant continuoustime linear control systems. It builds on previous works in the field, extending treatment of the system transfer functions, stability issues, the plant–control relationship, and control synthesis.
ADVANCES IN THE LINEAR DYNAMIC SYSTEMS THEORY
By: Lyubomir T. Gruyitch
Subjects: Engineering  Electrical, Engineering  Mechanical, Mathematics
ADVANCES IN THE LINEAR DYNAMIC SYSTEMS THEORY
Lyubomir T. Gruyitch
www.llumina.com/store/advancesinlineardynamics.htm
Llumina Press, 2013, www.llumina.com
ABSTRACT
The discovery of the full transfer function matrix F(s) of the linear dynamic system eliminates the deep and essential lacuna of their existing theory. It describes in the complex domain how the system simultaneously transmits and transfers both the action of the input vector and the influence of all initial conditions on the system output behavior. It has exactly the same properties as the classical system transfer function matrix G(s) that is valid only under all zero initial conditions. The full transfer function matrix is determined (together with all its submatrices) for the three classes of the systems, one of which is newly discovered.
The full transfer function matrix F(s) is the basis for the new, full (complete), block diagram system technique. It is established in this book. It essentially broadens the use and application of the classical block diagram technique that holds for zero initial conditions by its definition. The complete block diagram technique, being defined and developed for arbitrary initial conditions, fully overcomes the severe restriction of the classical block diagram technique.
Since Lyapunov stability properties are defined for nonzero initial conditions then their tests should be carried out by using F(s) because the use of G(s) can give the result opposite to the correct one, i.e. the result obtained via G(s) can be that the system is stable in spite it is unstable. The test via F(s) overcomes this problem.
BIBO stability was defined for zero initial conditions in order to test it effectively by using G(s). Initial conditions are almost always different from zero. Allowing nonzero initial conditions various new stability properties under boundedinput and for bounded arbitrary initial conditions are discovered and defined in this book. Their tests should be carried out by using F(s). G(s) is inapplicable.
For both Lyapunov stability properties and boundedinput and nonzero bounded initial conditions the new stability criteria proved in the book are in terms of F(s).
The book establishes the new system fundamental in the complex domain. It is inherent for the system stabilization and/or optimization. The discovers and the contributions of the book should essentially complete the university course in linear both control systems and dynamical systems. They open new avenues for research.
The book is equally significant and useful for lecturers, students, researchers as for linear dynamic system designers, control and system engineers.
Videos
Published: Jun 26, 2013
Definition and properties of time, links with other physical variables. Inconsistencies, paradoxes and mistakes of Einstein`s relativity theory. Novel, consistent, relativity theory. http://www.truthscience.info/time_and_consistent_relativity_theory
Published: Jun 26, 2013
Definition and properties of time, links with other physical variables. Inconsistencies, paradoxes and mistakes of Einstein`s relativity theory. Novel, consistent, relativity theory. http://www.truthscience.info/time_and_consistent_relativity_theory
Published: Jun 26, 2013
Definition and properties of time, links with other physical variables. Inconsistencies, paradoxes and mistakes of Einstein`s relativity theory. Novel, consistent, relativity theory. http://www.truthscience.info/time_and_consistent_relativity_theory
Published: Jun 26, 2013
Definition and properties of time, links with other physical variables. Inconsistencies, paradoxes and mistakes of Einstein`s relativity theory. Novel, consistent, relativity theory. http://www.truthscience.info/time_and_consistent_relativity_theory
Published: Jun 26, 2013
Definition and properties of time, links with other physical variables. Inconsistencies, paradoxes and mistakes of Einstein`s relativity theory. Novel, consistent, relativity theory. http://www.truthscience.info/time_and_consistent_relativity_theory
Published: Jun 26, 2013
Definition and properties of time, links with other physical variables. Inconsistencies, paradoxes and mistakes of Einstein`s relativity theory. Novel, consistent, relativity theory. http://www.truthscience.info/time_and_consistent_relativity_theory
Published: Jun 26, 2013
Definition and properties of time, links with other physical variables. Inconsistencies, paradoxes and mistakes of Einstein`s relativity theory. Novel, consistent, relativity theory. http://www.truthscience.info/time_and_consistent_relativity_theory
Published: Jun 26, 2013
Definition and properties of time, links with other physical variables. Inconsistencies, paradoxes and mistakes of Einstein`s relativity theory. Novel, consistent, relativity theory. http://www.truthscience.info/time_and_consistent_relativity_theory
Published: Jun 26, 2013
Definition and properties of time, links with other physical variables. Inconsistencies, paradoxes and mistakes of Einstein`s relativity theory. Novel, consistent, relativity theory. http://www.truthscience.info/time_and_consistent_relativity_theory
Published: Jun 26, 2013
Definition and properties of time, links with other physical variables. Inconsistencies, paradoxes and mistakes of Einstein`s relativity theory. Novel, consistent, relativity theory. http://www.truthscience.info/time_and_consistent_relativity_theory
Published: Jun 26, 2013
Definition and properties of time, links with other physical variables. Inconsistencies, paradoxes and mistakes of Einstein`s relativity theory. Novel, consistent, relativity theory. http://www.truthscience.info/time_and_consistent_relativity_theory
Published: Jun 26, 2013
Definition and properties of time, links with other physical variables. Inconsistencies, paradoxes and mistakes of Einstein`s relativity theory. Novel, consistent, relativity theory. http://www.truthscience.info/time_and_consistent_relativity_theory
Published: Jun 01, 2013
The first lecture in Serb of the invited conference by Professor Lyubomir T. Gruyitch at the Faculty of Mechanical Engineering, Kralyevo, Serbia, 2010. New discoveries on time, links among time, physical variables, dynamical systems with multiple time scales and systems control. Novel, consistent, relativity theory. See for more details: http://www.trurhscience.info
Published: Jun 01, 2013
The second lecture in Serb of the invited conference by Professor Lyubomir T. Gruyitch at the Faculty of Mechanical Engineering, Kralyevo, Serbia, 2010. New discoveries on time, links among time, physical variables, dynamical systems with multiple time scales and systems control. Novel, consistent, relativity theory. See for more details: http://www.trurhscience.info
Published: Jun 01, 2013
The third lecture in Serb of the invited conference by Professor Lyubomir T. Gruyitch at the Faculty of Mechanical Engineering, Kralyevo, Serbia, 2010. New discoveries on time, links among time, physical variables, dynamical systems with multiple time scales and systems control. Novel, consistent, relativity theory. See for more details: http://www.trurhscience.info
Published: Jun 01, 2013
The fourth lecture in Serb of the invited conference by Professor Lyubomir T. Gruyitch at the Faculty of Mechanical Engineering, Kralyevo, Serbia, 2010. New discoveries on time, links among time, physical variables, dynamical systems with multiple time scales and systems control. Novel, consistent, relativity theory. See for more details: http://www.trurhscience.info
Published: Jun 01, 2013
The fifth and sixth lecture in Serb of the invited conference by Professor Lyubomir T. Gruyitch at the Faculty of Mechanical Engineering, Kralyevo, Serbia, 2010. New discoveries on time, links among time, physical variables, dynamical systems with multiple time scales and systems control. Novel, consistent, relativity theory. See for more details: http://www.trurhscience.info