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Static output feedback controllers: Stability and convexity. (English) Zbl 0952.93106
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 2 LC 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:
93D15Stabilization of systems by feedback
93B40Computational methods in systems theory
93B52Feedback control
90C25Convex programming