This book covers crucial lacunae of the linear discrete-time time-invariant 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 well-known systems, IO and ISO, along with a new system, IIO. It discovers the concept of the full transfer function matrix F(z) in the z-complex domain, which incorporates the Z-transform 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 Z-transform 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 discrete-time time-invariant system, for short systems.
Additional information
Weight
0.86 kg
Product Properties
Year of Publication
2018
Table of Contents
Part I Basic Topics
1 Introduction
1.1 Discrete time, physical variables, and systems
1.2 Discrete time and system dynamics
1.3 Discrete-time systems and complex domain
1.4 Notational preliminaries
2 Classes of discrete-time linear systems
2.1 IO systems
2.2 ISO systems
2.3 IIO systems
2.4 System forms
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(z)
Part II Full Transfer Function Matrix F(z) And System Realization
5 Problem statement
6 Nondegenerate matrices
7 Definition of F(z)
7.1 Definition of F(z) in general
7.2 Definition of F(z) of the IO system
7.3 Definition of F(z) of the ISO system
7.4 Definition of F(z) of the IIO system
8 Determination of F(z)
8.1 F(z) of the IO system
8.2 F(z) of the ISO system
8.3 F(z) of the IIO system
8.4 Conclusion: Common general form of F(z)
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(z)
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(z)
12.1 Dynamical and least dimension of a system
12.2 On realization and minimal realization
12.3 Realizations of F(z) of IO systems
12.4 Realizations of F(z) of ISO systems
12.5 Realizations of F(z) of IIO systems
Part III Stability Study
13 Lyapunov stability
13.1 Lyapunov stability concept
13.2 Definitions
13.3 Lyapunov method and theorems
13.4 Conditions via F(z)
14 Bounded Input stability
14.1 BI stability and initial conditions
14.2 Definitions
14.3 Conditions
15 Motivation for the book
16 Summary of the contributions
17 Future teaching and research
V Bibliography
VI Appendices
A Notation
A.1 Abbreviations
A.2 Indexes
A.3 Letters
A.4 Names
A.5 Symbols and vectors
A.6 Units
B Z-transforms and unit impulses
B.1 Z-transforms
B.2 Unit impulses
Part VII Index
Author Index
Subject Index
Author
Zoran M Buchevats
ISBN/ISSN
9781138039599
Binding
Hardback
Edition
1
Publisher
CRC Press
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