Reachable Set Synthesis of Markov Jump Systems With Time-Varying Delays and Mismatched Modes

This note addresses the problem of reachable set synthesis of discrete-time Markov jump systems (MJSs) with time-varying delays and mismatched modes. The objective is to design suitable controllers to ensure the reachable set of the resulting closed-loop MJS is bounded by a prescribed set. First, by taking time-varying delays and mismatched modes into consideration, an ellipsoidal description of the reachable set is presented, which includes actual reachable states of the closed-loop MJS starting from the origin. Then, based on the description above, asynchronous reachable set controller parameters can be obtained if a set of linear matrix inequalities are feasible. Finally, an example is given to verify the validity of the obtained results.