Parametrization of stabilizing and robust stabilizing output feedback controllers for jump linear discrete-time systems

The paper considers a class of jump discrete-time control systems, described by a set of systems with the transition between them 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 individual linear dynamic corrupted by state and control dependent noises. A parametrization of all linear output feedback controllers which stabilize the system in the mean square sense is presented. Necessary and sufficient conditions for static output feedback controller with only mode dependent gain matrix to be robust stabilizing one against the mode change uncertainty are obtained. A heuristic LMI based algorithm for computation of the gain matrix of this controller is also given.