Exponential stability for discrete-time singular stochastic systems with semi-Markovian switching

In this paper, the stability of stochastic discrete-time singular systems with semi-Markovian switching (SMS) is taken into consideration. Based on inherent mode-dependent state jump behaviors, a time-dependent coordinate transformation is established, which is of great importance in discussion. Stochastic disturbances are also considered. Constructing Lyapunov function and applying stochastic analysis techniques, sufficient conditions for exponential stability in mean square and almost surely exponential stability are obtained by considering the probability density function of sojourn-time. Besides, we provide corresponding linear matrix inequalities (LMIs) of the provided sufficient conditions. Finally, the correctness of the results is demonstrated with an example.