Sliding mode control for stochastic Markovian jumping systems with incomplete transition rate

This study investigates the problem of sliding mode control for a class of stochastic Markovian jumping systems with partially known transition rate. A key feature in this work is to relax the requirement that all the elements in transition rate matrix are known, which does not always hold in actual applications. The finite set of modes is firstly divided into two parts, respectively, with known transitions rate and unknown one. Then, the sliding mode controller is designed to cope with the effect of partially known transition rate, in which two different robust terms are proposed, respectively, for the known and unknown modes. It is shown that both the reachability and asymptotic stability of sliding mode dynamics can be ensured by the present method, despite the partially known transition rate. Finally, numerical simulation results are given.