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.

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

##### MSC:

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 |