Stability and static output feedback stabilization for nonlinear discrete-time descriptor Markov jump systems with time-varying delay

In this paper, stability and static output feedback stabilization for nonlinear discrete-time descriptor Markov jump systems with time-varying delay is discussed. First, based on Lyapunov theory and the implicit function theorem, a linear matrix inequality (LMI) sufficient condition is developed which guarantees that the nonlinear discrete-time descriptor Markov jump systems with time-varying delay are regular, causal, have unique solution in a neighborhood of the equilibrium point, and are stochastically stable. In order to facilitate the design of the controller, with this condition, by using a series of matrix inequalities, another LMI stability condition is obtained. Then, by using singular value decomposition approach, and the design method of static output feedback controllers is given. Last, a numerical example is given to show the effectiveness and correctness of the proposed method.