Mathematical methods of control theory. Problems of stability, controllability and observability
type: Item
instance of: scholarly article
zbMATH Open document ID: 1302.93001
author: A. S. Fursov
author: S. V. Emel'yanov
author: S. K. Korovin
author: A. V. Il'in
author: V. V. Fomichev
publication date: 2014-10-16T00:00:00Z
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93B07
Mathematics Subject Classification ID: 93B10
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 34H05
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 6356786
zbMATH Keywords: control systems
zbMATH Keywords: stability
zbMATH Keywords: controllability
zbMATH Keywords: observability
MaRDI profile type: Publication
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title: Mathematical methods of control theory. Problems of stability, controllability and observability
review text: The subject of the book is related to the theory of linear control systems including both autonomous and non-autonomous systems.NEWLINENEWLINEThe book contains four chapters. Chapter 1, ''Description of control systems'', contains some basic concepts. In particular, notions of controlled object, transfer function, time and frequency characteristics are introduced. Chapter 2,'' Stability of continuous systems'', is devoted to the investigation of the problem of stability of linear dynamical systems, autonomous and non-autonomous. Problems of stability of uncertain systems and stability with respect to a part of variables are discussed, too. Chapter 3, ''Controllability and observability'', deals with the problems of controllability and observability for autonomous and non-autonomous systems. In Chapter 4, ''Canonical forms, reducibility and elements of the realization theory'', canonical representations of linear autonomous control systems and elements of the realization theory are introduced and analyzed. Two appendices, ''Elements of complex analysis'' and ''Some concepts related to theory of matrices and polynomials'', successfully complete the book.NEWLINENEWLINEThere are many exercises throughout the book. These range from computational exercises to assist the reader in fixed ideas, to extensions of the theory not developed in the text.NEWLINENEWLINEThe book addresses graduate students and researchers in advanced control engineering, applied mathematics and mathematical systems theory.
description: scientific article; zbMATH DE number 6356786