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Zbl 0952.93106
Geromel, J.C.; de Souza, C.C.; Skelton, R.E.
Static output feedback controllers: Stability and convexity. (English)
[J] IEEE Trans. Autom. Control 43, No.1, 120-125 (1998). ISSN 0018-9286

Summary: The main objective of this paper is to solve the following stabilizing output feedback control problem: Given matrices $(A,B_2,C_2)$ with appropriate dimensions, find (if one exists) a static output feedback gain $L$ such that the closed-loop matrix $A-B_2LC_2$ is asymptotically stable. It is known that the existence of $L$ is equivalent to the existence of a positive definite matrix belonging to a convex set such that its inverse belongs to another convex set. Conditions are provided for the convergence of an algorithm which decomposes the determination of the aforementioned matrix in a sequence of convex programs. Hence, this paper provides a new sufficient (but not necessary) condition for the solvability of the above stabilizing output feedback control problem. As a natural extension, we also discuss a simple procedure for the determination of a stabilizing output feedback gain assuring good suboptimal performance with respect to a given quadratic index. Some examples borrowed from the literature are solved to illustrate the theoretical results.

MSC 2000:: *93D15 Stabilization of systems by feedback
93B40 Computational methods in systems theory
93B52 Feedback control
90C25 Convex programming

Keywords: stabilization; output feedback control; algorithm; convex programs

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