Publisher's Synopsis
The main aim of this book is to present recent developments in multivariable one-dimensional (1-D) and multidimensional linear system theory. Special attention is devoted to polynomial-equation methods. The book consists of two volumes. In the first volume, 1-D linear systems are analyzed. The second volume is devoted to the synthesis of multivariable systems and multidimensional systems. The first volume is organized as follows: In chapter 1, solvability conditions of generalized discrete-time and continuous-time 1-D linear systems and methods of finding their solutions are given. The reduction of singular systems to their canonical forms is considered. Transfer matrices, matrix-fraction descriptions, system matrices and their equivalence are also studied.;The reachability, controllability, observability and constructibility of generalized linear systems are described in Chapter 2. Tests for checking the output-reachability and observability of composite systems described by differential (difference) operators are given. Different notions of reachability, controllability and observability of linear singular systems are developed.;Chapter 3 is devoted to the canonical forms of linear multivariable 1-D systems. Relationships among the canonical forms and Kalman's canonical-structure theorem are also presented.;The realization problem of transfer matrices for generalized linear systems is considered in chapter 4. Existence conditions and procedures for finding minimal realization and realizations in canonical forms are given. The realization problem for linear systems described by differential (difference) operators and realization in the Weierstrass canonical form are also considered.;Chapter 5 gives definitions and relationships between different poles and zeros of systems and transfer matrices. The system zeros, invariant zeros, decoupling zeros, blocking zeros, system poles, transmission poles and relationships between them are examined. Infinite poles and zeros of transfer matrices and systems are also discussed.
