Linear discrete-time systems

"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."--Provided by publisher.

Chapter 1 Part I BASIC TOPICS -- chapter 1 Introduction -- chapter 2 Classes of discrete-time linear systems -- chapter 3 System regimes -- chapter 4 Transfer function matrix G(z) -- chapter 2 Part II FULL TRANSFER FUNCTIONMATRIX F(z) AND SYSTEM REALIZATION -- chapter 5 Problem statement -- chapter 6 Nondegenerate matrices -- chapter 7 Definition of F(z) -- chapter 8 Determination of F(z) -- chapter 9 Full block diagram algebra -- chapter 10 Physical meaning of F(z) -- chapter 11 System matrix and equivalence -- chapter 12 Realizations of F(z) -- chapter 3 Part III STABILITY STUDY -- chapter 13 Lyapunov stability -- chapter 14 Bounded input stability -- chapter 4 Part IV CONCLUSION -- chapter 15 Motivation for the book -- chapter 16 Summary of the contributions -- chapter 17 Future teaching and research -- chapter 5 Part V APPENDICES.