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Singular control systems. (English) Zbl 0669.93034
Lecture Notes in Control and Information Sciences, 118. Berlin etc.: Springer-Verlag. ix, 332 p. DM 77.00 (1989).
The book is devoted to singular linear time-invariant systems, i.e. systems of the form \(E\dot x=Ax+Bu\), \(y=Cx\), where the matrix E is singular. It collects many results scattered in the literature, some of them due to the author.
Chapter 1 contains preliminaries concerning singular linear differential equations. Chapter 2 studies basic properties of singular systems as reachability, controllability, observability, system decomposition, transfer matrix, minimal realization. Chapter 3 is devoted to pole placement by linear feedback. The state observation by singular and “normal” observers is discussed in Chapter 4. In Chapter 5 the dynamic compensation problem for singular systems is studied. Chapter 6 deals with structural stability. The transfer function approach is outlined in Chapter 7. Chapter 8 contains an introduction to discrete-time singular systems, that is \(Ex(k+1)=Ax(k)+Bu(k)\). Chapter 9 focusses some aspects of optimal control.
The book is addressed mainly to control and systems engineers. It requires some basic knowledge on linear algebra and linear control theory.
Reviewer: A.Dontchev

93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
93C05 Linear systems in control theory
34A99 General theory for ordinary differential equations
93C15 Control/observation systems governed by ordinary differential equations
93C55 Discrete-time control/observation systems