Sliding mode control for Markovian jumping systems with time delays

Abstract This chapter focuses on the sliding mode observer (SMO)-based robust control problem for a class of Ito stochastic MJSs with output disturbances and time delays. First, we will construct a proportional-derivative SMO and synthesize an SMO-based controller. Then, for the purpose of guaranteeing the stochastic stability for the closed-loop plant, we will propose Theorem 1 . Furthermore, Theorem 2 is derived to ensure the reachability of the sliding mode surface. During these procedures, we can solve the controller gain and the observer coefficients in only one linear matrix inequality problem which reduces the computational load and the design complexity. In addition, by employing the proposed descriptor SMO, we can identify the disturbance directly.