Stabilization of Time-Delay Markovian Jump Systems Via Probability Rate Synthesis and State Feedback

This paper considers the stabilization problem for Markovian jump systems with time delays. Both the probability rate matrix and the state feedback control law are to be designed. A sufficient condition is established for such designs such that the resulting closedloop Markovian jump system is stochastically stable. This condition is given in terms of a system of linear matrix inequalities with rank constraints, and can be solved using some existing algorithms. When the system has polytopic uncertainties, the robust stabilization problem is studied as well. Finally, a numerical example is given to show the validity of the proposed method.