LQR parametrization of static output feedback gains for linear systems with Markovian switching and related robust stabilization and passification problems

The purpose of this paper is a parametric description (parametrization) of static output feedback stabililizing controllers for linear continuous-time systems with Markovian switching. The results are then applied to simultaneous stabilization, robust stabilization and passification problems. Based on these results some algorithms for computing of stabilizing gains are proposed. The approach is based on a parametrization in terms of coupled linear matrix equations and quadratic matrix inequalities which depend on parameter matrices similar to weight matrices in LQR theory. The problem is non-convex in general but using a convexifying approximation technique the algorithms are LMI-based. These are non-iterative and used computationally efficient SDP solvers.