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Linear control systems. Volume 1: Analysis of multivariable systems. (English) Zbl 0784.93002
Industrial Control Computers and Communications Series. 6. Taunton: Research Studies Press Ltd.. New York: John Wiley & Sons Inc.. xix, 379 p. (1992).
The main aim of this book is to present recent developments in multidimensional linear system theory. In the first volume, one- dimensional linear systems are analysed. This volume is organised as follows: In Chapter 1, solvability conditions of generalised discrete- time and continuous-time one-dimensional linear systems and methods of finding their solutions are given. The reduction of singular systems to their canonical forms is considered. Transfer matrices, system matrices and their equivalence are also studied. The reachability, controllability, observability and constructibility of generalised linear systems are described in Chapter 2.
Chapter 3 is devoted to the canonical forms of linear multivariable one- dimensional systems. Relationships among the canonical forms and Kalman’s canonical-structure theorem are also presented. The realisation problem of transfer matrices for generalised linear systems is considered in Chapter 4. Chapter 5 gives definitions and relationships between different poles and zeros of systems and transfer matrices.
In each chapter, there are many illustrative examples. To complete the book, three appendices are included.
Reviewer: S.Anita (Iaşi)

93-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory
93B05 Controllability
93B07 Observability
93B55 Pole and zero placement problems
93C35 Multivariable systems, multidimensional control systems
93B10 Canonical structure