# Linear Discrete-Time Systems

DOI link for Linear Discrete-Time Systems

Linear Discrete-Time Systems book

# Linear Discrete-Time Systems

DOI link for Linear Discrete-Time Systems

Linear Discrete-Time Systems book

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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

**(z) and the full block diagram technique based on the use of**

*P***(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**

*F**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.

## TABLE OF CONTENTS

part I|98 pages

Basic Topics

chapter 2|21 pages

#### Chapter2: Classes of discrete‐time linear systems

chapter 4|2 pages

#### Chapter 4: Transfer function matrix G (z)

part II|154 pages

Full Transfer Function Matrix F(z) and System Realization

chapter 11|18 pages

#### Chapter 11: System matrix and equivalence

part III|132 pages

Stability Study

part IV|9 pages

Conclusion