An anti-windup design to robust H∞ control for singular Markovian jump systems with actuator saturation and general unknown transition rates

This paper is concerned with the problem of robust H∞ control for a class of singular Markovian jump systems (SMJSs) with generally uncertain transition rates (GUTRs) and actuator saturation via anti-windup design. In this GUTR model, each transition rate can be completely unknown or only its estimate value is known. Under the assumption that a set of linear dynamic output feedback controllers have been designed to stabilize the SMJSs in the absence of actuator saturation, anti-windup compensators are designed to impair the actuator saturation effect on the closed-loop systems subject to admissible external disturbances, Itô-type stochastic disturbances, transition rate and norm-bounded parameter uncertainties. Anti-windup compensation gains can be derived via solving a convex optimization problem with constraints of a set of linear matrix inequalities (LMIs). Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed method.