Control systems. From linear analysis to synthesis of chaos. (English) Zbl 0874.93006

Vaněček, Antonín; Čelikovský, S.

Prentice Hall International Series in Systems and Control Engineering. London: Prentice Hall. x, 277 p. (1996).

The study of dynamical systems is a subject of extremely large interest for many scientists from different domains of activity. There are several fundamental ideas developed in the present book. Some of them consist of how we might investigate the behaviour of linear control systems subjected to large changes in several system parameters, how we might use symmetry to optimize a linear control system and to make the numerical computations robust, how we might proceed from the linear case to the nonlinear one and why the synthesis of chaotic behaviour might be desirable in some cases.
The presented book contains eight big chapters, as follows: Systems, Systems with action of parameters, Systems with single variable control, Systems with multivariable control, Systems with symmetric control, Systems II, Systems with weakly nonlinear control, and Systems with strongly nonlinear control. It is structured and conceived both as a history of the most important results and as an excellent guide in the world of chaos.
The book contains more than 30 definitions, more than 60 theorems, corollaries and lemmas and about 120 examples and remarks. The purpose of this accurate presentation is to strongly understand the complex behaviour of dynamical systems and there are no doubts that this work represents an extremely useful instrument both for beginners and experienced researchers.
Remark: Please allow me to tell you there is a small typographical mistake on page 157: 8. Survey of classical matrix groups and algebras.

Reviewer: I.Grosu (Iaşi)

MSC:

93-02	Research exposition (monographs, survey articles) pertaining to systems and control theory
37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93C05	Linear systems in control theory
93C10	Nonlinear systems in control theory

Keywords:

control; synchronization; stabilization; symmetry; synthesis of chaotic behaviour