Control theory for linear systems Harry L. Trentelman Research Institute of Mathematics and Computer Science University of Groningen P.O. Box 800, 9700 AV Groningen The Netherlands Tel. +31-50-3633998 Fax. +31-50-3633976 E-mail.
[email protected] Anton A. Stoorvogel Dept. of Mathematics and Computing Science Eindhoven Univ. of Technology P.O. Box 513, 5600 MB Eindhoven The Netherlands Tel. +31-40-2472378 Fax. +31-40-2442489 E-mail.
[email protected] Malo Hautus Dept. of Mathematics and Computing Science Eindhoven Univ. of Technology P.O. Box 513, 5600 MB Eindhoven The Netherlands Tel. +31-40-2472628 Fax. +31-40-2442489 E-mail.
[email protected]
ISBN-10: 1852333162
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Preface This book originates from several editions of lecture notes that were used as teaching material for the course ‘Control Theory for Linear Systems’, given within the framework of the national Dutch graduate school of systems and control, in the period from 1987 to 1999. The aim of this course is to provide an extensive treatment of the theory of feedback control design for linear, finite-dimensional, time-invariant state space systems with inputs and outputs. One of the important themes of control is the design of controllers that, while achieving an internally stable closed system, make the influence of certain exogenous disturbance inputs on given to-be-controlled output variables as small as possible. Indeed, in the appropriate sense this theme is covered by the classical linear quadratic regulator problem and the linear quadratic Gaussian problem, as well as, more recently, by the H 2 and H∞ control problems. Most of the research efforts on the linear quadratic regulator problem and the linear quadratic Gaussian problem took place in the period up to 1975, whereas in particular H ∞ control has been the important issue in the most recent period, starting around 1985. In, roughly, the intermediate period, from 1970 to 1985, much attention was attracted by control design problems that require to make the influence of the exogenous disturbances on the to-be-controlled outputs equal to zero. The static state feedback versions of these control design problems, often called disturbance decoupling, or disturbance localization, problems were treated in the classical textbook ‘Linear Multivariable Control: A Geometric Approach’, by W.M. Wonham. Around 1980, a complete theory on the disturbance decoupling problem by dynamic measurement feedback became available. A central role in this theory is played by the geometric (i.e., linear algebraic) properties of the coefficient matrices appearing in the system equations. In particular, the notions of (A, B)-invariant subspace and (C, A)invariant subspace pl