1st Edition

# Linear Continuous-Time Systems

By

## Lyubomir T. Gruyitch

ISBN 9781138039506
Published May 26, 2017 by CRC Press
469 Pages

USD \$165.00

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## Book Description

This book aims to help the reader understand the linear continuous-time time-invariant 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 continuous-time time-invariant systems, for short systems.

Contents

Dedication

Preface

0.1 On the state of the art

0.2 On the book

0.3 In gratitude

Part I BASIC TOPICS OF LINEAR CONTINUOUS-TIME

TIME-INVARIANT DYNAMICAL SYSTEMS

1 Introduction

1.1 Time

1.2 Time, physical principles, and systems

1.3 Time and system dynamics

1.4 Systems and complex domain

1.5 Notational preliminaries

2 Classes of systems

2.1 IO system

2.2 ISO systems

2.3 IIO systems

3 System Regimes

3.1 System regime meaning

3.2 System regimes and initial conditions

3.3 Forced and free regimes

3.4 Desired regime

3.5 Deviations and mathematical models

3.6 Stationary and nonstationary regimes

3.7 Equilibrium regime

4 Transfer function matrix G(s)

Part II FULL TRANSFER FUNCTION MATRIX F(S) AND

SYSTEM REALIZATION

5 Problem statement

6 Nondegenerate matrices

7 Definition of F(s)

7.1 Definition of F(s) in general

7.2 Definition of F(s) of the IO system

7.3 Definition of F(s) of the ISO system

7.4 Definition of F(s) of the IIO system

8 Determination of F(s)

8.1 F(s) of the IO system

8.2 F(s) of the ISO system

8.3 F(s) of the IIO system

8.4 Conclusion: Common general form of F(s)

9 Full block diagram algebra

9.1 Introduction

9.2 Parallel connection

9.3 Connection in series

9.4 Feedback connection

10 Physical meaning of F(s)

10.1 The IO system

10.2 The ISO system

10.3 The IIO system

11 System matrix and equivalence

11.1 System matrix of the IO system

11.2 System matrix of the ISO System

11.3 System matrix of the IIO system

12 Realizations of F(s)

12.1 Dynamical and least dimension of a system

12.2 On realization and minimal realization

12.3 Realizations of F(s) of IO systems

12.4 Realizations of F(s) of ISO systems

12.5 Realizations of F(s) of IIO systems

Part III STABILITY STUDY

13 Lyapunov stability

13.1 Lyapunov stability concept

13.2 Lyapunov stability definitions

13.3 Lyapunov method and theorems

13.4 Lyapunov stability conditions via F(s)

14 Bounded Input stability

14.1 BI stability and initial conditions

14.2 BI stability definitions

14.3 BI stability conditions

Part IV CONCLUSION

15 Motivation for the book

16 Summary of the contributions

17 Future teaching and research

Part V Appendices

A Notation

A.0.4 Abbreviations

A.0.5 Indexes

A.0.6 Letters

A.0.7 Names

A.0.8 Symbols and vectors

A.0.9 Units

B From IO system to ISO system

C From ISO system to IO system

D Relationships among system descriptions

E Laplace transforms and Dirac impulses

E.1 Laplace transforms

E.2 Dirac impulses

F Proof of Theorem 142

G Example: F(s) of a MIMO system

H Proof of Theorem 165

I Proof for Example 167

J Proof of Theorem 168

K Proof of Theorem 176

L Proof of Theorem 179

M Proof of Theorem 183

Author Index

Subject Index

...

## Author(s)

### Biography

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 -UB, Serbia). 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 division and research Laboratory of Automatic Control of the Faculty of Mechanical Engineering, UB . He has given invited university seminars in Belgium, Canada, England, France, Russia, Serbia, Tunis, and USA. He has published 8 books (7 in English, 1 in Serb), 4 textbooks (in Serbo-Croatian), 11 lecture notes (7 in French, 2 in English, 2 in Serbo-Croatian), one manual of solved problems, one book translation from Russian, chapters in eight scientific books, 130 scientific papers in scientific journals, 173 conference research papers, and 2 educational papers. France honored him Doctor Honoris Causa (DHC).

### Featured Author Profiles

Author

#### Lyubomir T. Gruyitch

Retired University Professor, Retired with the University of Technology Belfort-Montbeliard (UTBM), Belfort, France