Robust Stabilization of Jump Polytopic Systems via Output Feedback

The paper considers a class of systems composed of a finite set of linear plants with jumping transition between them determined by a homogeneous Markov chain. Each state of this chain corresponds to some mode of the system. Necessary and sufficient conditions for robust stabilization against polytopic uncertainty of modes and for simultaneous stabilization via output feedback are obtained. Some algorithms for computation of gain matrices of stabilizing controllers are given, along with an illustrative example. The algorithms effectively use LMI solvers.