Static output feedback controllers: stability and convexity

The main objective of this paper is to solve the following stabilizing output feedback control problem: given matrices (A; B₂ ; C₂) with appropriate dimensions, find (if one exists) a static output feedback gain L such that the closed-loop matrix A-B₂LC₂ 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