Rolewicz, Stefan Functional analysis and control theory. Linear systems. (Transl. from the Polish). (English) Zbl 0633.93002 Mathematics and its Applications (East European Series), 29. Dordrecht etc.: D. Reidel Publishing Company, a member of the Kluwer Adademic Publishers Group; Warszawa: PWN - Polish Scientific Publishers. XV, 524 p.; Dfl. 295.00; $ 118.00; £118.00; £80.95 (1987). The present book gives a very good exposition of the applications of functional analysis to control and optimization theory. The contents are divided into eight chapters. The first four chapters of the book can be treated as a short course of functional analysis, where engineering and economical interpretations of the fundamental notions are given. In the fifth chapter the theory of general linear systems is developed. Chapter 6 contains applications of the theory developed in Chapter 5 to systems described by ordinary differential equations. Chapter 7 presents applications to systems described by partial differential equations. The last chapter is concerned with the problems of stability and optimal controllability for systems described by differential equations in Banach spaces. This book is addressed not only to mathematicians but also to engineers, economists and other specialists interested in optimization and control theory. Reviewer: M.Megan Cited in 12 Documents MSC: 93-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory 93C05 Linear systems in control theory 93C25 Control/observation systems in abstract spaces 46B99 Normed linear spaces and Banach spaces; Banach lattices 49J27 Existence theories for problems in abstract spaces 93C15 Control/observation systems governed by ordinary differential equations 93C20 Control/observation systems governed by partial differential equations 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory Keywords:applications of functional analysis to control and optimization PDFBibTeX XML