Robust stabilization of jumping system via static output feedback

The paper considers a class of control systems, described by a finite set of linear systems with the transition between them determined by a homogeneous Markov chain. Every state of this chain correspond to some mode of the system. When the mode is fixed, the plant state evolves according to the corresponding individual dynamic. At the moment of discontinuous mode change the plant state vector can be changed by jump. The necessary and sufficient conditions of stabilizability in the mean square via static output feedback control are formulated. These conditions are generalized to the case of the mode change parameters uncertainty. The sufficient conditions which guarantee, that the static output feedback control stabilizes the system for plant parameters uncertainty are obtained. Some heuristic algorithms for computing of the gain matrix of robust stabilizing control are also developed.