Static Output-Feedback Control of Markov Jump Linear Systems Without Mode Observation

Abstract

In this paper, we address infinite-horizon optimal control of Markov Jump Linear Systems (MJLS) via static output feedback. Because the jump parameter is assumed not to be observed, the optimal control law is nonlinear and intractable. Therefore, we assume the regulator to be linear. Under this assumption, we first present sufficient feasibility conditions for static output-feedback stabilization of MJLS with nonobserved mode in the mean square sense in terms of linear matrix inequalities (LMIs). However, these conditions depend on the particular state-space representation, i.e., a coordinate transform can make the LMIs feasible, while the original LMIs are infeasible. To avoid the issues with the ambiguity of the state-space representation, we, therefore, present an iterative algorithm for the computation of the regulator gain. The algorithm is shown to converge if the MJLS is stabilizable via mode-independent static output feedback. However, convergence of the algorithm is not sufficient for the stability of the closed loop, which requires an additional stability check after the regulator gains have been computed. A numerical example demonstrates the application of the presented results.