LMI numerical solution for output feedback stabilization

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. Using linear matrix inequalities, it is shown 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 global convergence of the min/max algorithm which decomposes the determination of the aforementioned matrix by a sequence of convex programs. Some examples borrowed from the literature are solved hi order to illustrate the theoretical results.