Sliding mode control of Markovian jump systems with incomplete information on time-varying delays and transition rates

This paper is concerned with robust sliding mode control (SMC) for continuous-time Markovian jump delay systems with incomplete transition rates (TRs), the time-varying delays are unclear and just bounded sometimes. Two methods are employed to investigate this control issue. One is movement decomposition method by which reduced-order sliding mode dynamics is obtained; the other is via sliding mode observer and full-order sliding mode dynamics is obtained on the estimation space. In both cases, sufficient conditions are established in terms of a set of coupled linear matrix inequalities (LMIs) to ensure the sliding mode dynamics to be mean-square exponentially stable; moreover, novel sliding mode controllers, which need not full knowledge on time-varying delays, are synthesized to guarantee the reachability of the prescribed sliding surface. Finally, numerical examples are provided to illustrate the effectiveness of the proposed methods.