Stability analysis and control design of singular Markovian jump systems via a parameter-dependent reciprocally convex matrix inequality

This paper is concerned with the problems of stochastic stability and control design for singular Markovian jump systems (SMJSs) with time varying delay. The derivative coefficient is considered to be mode dependent. A parameter-dependent reciprocally convex matrix inequality (PDRCMI) is constructed, which covers some existing ones as its special cases. Different from some existing ones, the introduced parameters are completely known, which can be optimized by an iteration algorithm. To decrease the redundant decision variables, a mild assumption is given for the case of mode-dependent coefficient such that the considered system is decomposed into differential equations and algebraic ones. In this case, the components of state vectors of the subsystem are applied to construct a new augmented Lyapunov-Krasovkii functional (LKF). Based on the PDRCI and the new augmented LKF, a novel stochastic stability condition with both less computational demands and less conservativeness is derived. Based on the decomposed subsystems and the stability condition, a set of state feedback controller is designed in terms of linear matrix inequalities (LMIs). Some numerical examples are introduced to illustrate the effectiveness of the proposed results.