This paper investigates the sliding mode control scheme for a class of discrete singular semi-Markov jump systems with mode-dependent singular matrix. The singular systems are subjected to a semi-Markov chain characterized via discrete-time semi-Markov kernel, where the mode switching is determined by the transition probability and the sojourn-time distribution function. In light of the underlying system with mode-dependent singular matrix, novel stability criteria with reduced conservatism are established in terms of the original coefficient matrices by advancing the analysis theory. Then, sufficient conditions are derived in view of the -error mean-square stable sense. Moreover, a dedicated sliding mode control (SMC) scheme is constructed to enforce the reachability of the discrete quasi-sliding motion. Finally, the applicability of the control scheme is demonstrated through DC motor model.
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