Robust stabilizing control of discrete-time jumping system via static output feedback

The paper considers a class of hybrid-state discrete time control systems, described by a set of systems with the transition between then determined by a homogeneous Markov chain taking values in a finite set of modes. When the mode is fixed, the plant state evolves according to the corresponding individual linear dynamics. The necessary and sufficient conditions of stabilizability in the mean square via static output feedback control are obtained. In the case when the mode change process has uncertainties a robust version of these conditions is given. A heuristic LMI based algorithm for computation of static output feedback control is also given.