Time-Varying Discrete Linear Systems: Input-Output Operators. Riccati Equations. Disturbance Attenuation

by Aristide Halanay, Vlad Ionescu

Overview

Discrete-time systems arise as a matter of course in modelling biological or economic processes. For systems and control theory they are of major importance, particularly in connection with digital control applications. If sampling is performed in order to control periodic processes, almost periodic systems are obtained. This is a strong motivation to investigate the discrete-time systems with time-varying coefficients. This research monograph contains a study of discrete-time nodes, the discrete counterpart of the theory elaborated by Bart, Gohberg and Kaashoek for the continuous case, discrete-time Lyapunov and Riccati equations, discrete-time Hamiltonian systems in connection with input-output operators and associated Hankel and Toeplitz operators. All these tools aim to solve the problems of stabilization and attenuation of disturbances in the framework of H2- and H-control theory. The book is the first of its kind to be devoted to these topics and consists mainly of original, recently obtained results.

Product Details

ISBN-13:	9783764350123
Publisher:	Birkhäuser Basel
Publication date:	03/01/1994
Series:	Operator Theory: Advances and Applications , #68
Edition description:	1994
Pages:	230
Product dimensions:	6.69(w) x 9.61(h) x (d)

Table of Contents

0. General motivation.- 1. Evolutions and related basic notions.- 2. Nodes.- 3. Riccati equations and nodes.- 4. Disturbance Attenuation.- Appendix A. Discrete-time shastic control.- 1. Discrete-time Riccati equation of shastic control.- 2. Optimal compensator under independent random disturbances.- Notes and References.- Appendix B. Almost periodic discrete-time systems.- 1. Standeard theory of almost periodic sequences.- 2. A new Bochner theory for almost periodic sequences.- 3. Almost periodic evolution.- 4. Evolutions under Besicovitch sequences.- Notes and References.- References.

Editorial Reviews

This monograph emerged from an attempt to develop a time-variant discrete compensation theory for achieving both stabilization and disturbance attenuation. It studies discrete-time nodes; the discrete counterpart of the theory elaborated by Bart, Goberg and Kaashoek for the continuous case; discrete-time Lyapunov and Riccati equations; and discrete-time Hamiltonian systems in connection with input-output operators and associated Hankel and Toeplitz operators. The subject is of importance in connection with the modelling of biological or economic processes, sampling performed to control periodic processes, and systems and control theory, in particular, digital control applications. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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