Linear continuous-time systems

✍ Scribed by Lyubomir T. Gruyitch

• Publisher: CRC Press
• Year: 2017
• Tongue: English
• Leaves: 496
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Content: Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
List of Figures
Preface
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 systems
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
3.3.1 Introduction 3.7.3 ISO systems3.7.4 IIO systems
4: Transfer function matrix G(s)
II: FULL TRANSFER FUNCTION MATRIX F(S) AND SYSTEM REALIZATION
5: Problem statement
6: Nondegenerate matrices
7: Defnition of F(s)
7.1 Defnition of F(s) in general
7.2 Defnition of F(s) of the IO system
7.3 Defnition of F(s) of the ISO system
7.4 Defnition 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 series9.4 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
12.2.1 Minimal realization of the transfer function matrix
12.2.2 Realization and minimal realization of the full transfer function matrix and the system 12.3 Realizations of F(s) of IO systems12.4 Realizations of F(s) of ISO systems
12.5 Realizations of F(s) of IIO systems
III: STABILITY STUDY
13: Lyapunov stability
13.1 Lyapunov stability concept
13.2 Lyapunov stability definitions
13.2.1 IO systems
13.2.2 ISO systems
13.2.3 IIO systems
13.3 Lyapunov method and theorems
13.3.1 Outline of Lyapunov's original theory
13.3.2 Lyapunov method, theorems and methodology for the linear systems
13.3.3 Lyapunov theorem for the IO systems
13.3.4 Lyapunov theorem for the ISO systems
13.3.5 Lyapunov theorem for the IIO systems

✦ Subjects

Linear control systems.;Invariant manifolds.;Time-domain analysis.;MATHEMATICS / Calculus;MATHEMATICS / Mathematical Analysis