Stabilization of discrete-time singular Markovian jump repeated vector nonlinear systems

This paper studies the control problem for discrete-time singular Markovian jump systems with repeated vector nonlinearities. Sufficient conditions for stochastic stability are established, where the uniqueness of solution to the underlying system is also guaranteed. Then, a series of formulations of stabilizing conditions is further developed to design mode-dependent and mode-independent controllers by using the linear matrix inequality approach. Based on the proposed results, more special cases for stabilizing controller are considered. Finally, numerical examples are used to demonstrate the effectiveness and superiority of the proposed methods.