Robust stabilization of delayed Markovian jump systems subject to parametric uncertainties

The problems of robust stabilization and H_infin control for uncertain discrete-time Markovian jump linear systems with mode-dependent input time-delays are investigated in this paper. The descriptor system approach is employed to establish sufficient conditions for robust stabilization and the existence of H_infin delayed state feedback controller via a properly constructed stochastic Lyapunov functional. The derived sufficient conditions, which are expressed in the form of linear matrix inequalities, turn out to be simple. Moreover, these conditions are easily solvable by using some existing software packages. One numerical example is presented to illustrate the usefulness of the theoretical results.