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Linear Discrete-Time Systems

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ISBN: 9781138039599
Author/Editor: Zoran M Buchevats

Publisher: CRC Press

Year: 2018

1 in stock (can be backordered)

SKU: ABD-CRC-4214 Category:

Description

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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