Tracking Control of Linear Systems: 1st Edition (Hardback) book cover

Tracking Control of Linear Systems

1st Edition

By Lyubomir T. Gruyitch

CRC Press

423 pages | 22 B/W Illus.

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Hardback: 9781466587519
pub: 2013-05-29
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pub: 2018-10-03
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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 re-examining classic linear control systems theory. It then defines and determines the system full (complete) transfer function matrix F(s) for two classes of systems: input-output (IO) control systems and input-state-output (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 time-invariant continuous-time 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.

Table of Contents

On Control Systems Classic Fundamentals


Time, Physical Variables and Systems

Systems and Complex Domain

Notational Preliminaries

Control Systems

IO Control Systems

ISO Control Systems

System Regimes

System Regime Meaning

Forced and Free Regimes

Desired Regime

Transfer Function Matrix G(s)

On Definitions of G(s)

On Importance of G(s)

Novel System Fundamental: Full Transfer Function Matrix F(S)

Problem Statement

Nondegenerate Matrices

Nondegenerate and Degenerate Matrices

Basic Lemma

Full Transfer Function Matrix F(s)

General Definitions of F(S)

Determination of F(s) in General

F(s) of the IO Control System

F(s) of the ISO Control System

Conclusion: General Form of F(s)

Physical Meaning of F(s)

Novel Control Theories: Tracking and Trackability

Tracking Theory

Tracking Generally

Tracking versus Stability

Perfect Tracking: Characterization

Imperfect Tracking: Characterization

Trackability Theory

Trackability versus Controllability

Trackability Definitions

Perfect Trackability Conditions

Imperfect Trackability Conditions

Novel Synthesis of Tracking Control

Linear Tracking Control (LITC)

Generating Theorem

LITC of the IO Plants

LITC of the ISO Plants

Lyapunov Tracking Control (LTC)

Vector Lyapunov Function (VLF)

LTC of the IO Plant

LTC of the ISO Plant

Natural Tracking Control (NTC)

Concept of NTC

NTC of the IO Plant

NTC of the ISO Plant

NTC versus LTC

General Consideration

The IO Plant

The ISO Plant


On F(s)

On Tracking and Trackability

On Tracking Control







Names and Symbols


From IO system to ISO system

From ISO system to IO system

Proof of Theorem 64

Proof of Theorem 67

Proof of Theorem 72

Proof of Theorem 91

Proof of Lemma 102-Basic Lemma

Proof of Theorem 116

Proof of Theorem 142

Proof of Theorem 145

Proof of Theorem 149

Author Index

Subject Index

About the Originator


Lyubomir T. Gruyitch

Belgrade and Levallois Perret, , Serbia and France

Learn more about Lyubomir T. Gruyitch >>

Subject Categories

BISAC Subject Codes/Headings:
TECHNOLOGY & ENGINEERING / Power Resources / Electrical