SMC for discrete singular stochastic jump systems under semi-Markov kernel

In this study, the sliding mode control (SMC) is investigated for discrete singular stochastic semi-Markov jump systems under a semi-Markov kernel. Based on the remarkable application background and advantages in modeling complex dynamic systems, singular semi-Markov jump systems are utilized to address discrete SMC issues. A mode-dependent sliding function with a singular matrix is considered to reduce the effects of the numerical problems. The main aim is to use an improved approach to eliminate the matrix power terms so that the underlying augmented system can realize mean-square admissibility. An appropriate SMC law is constructed to achieve the reachability of the quasi-sliding mode, overcoming the difficulty caused by parameter uncertainty. Finally, the effectiveness of the SMC approach is verified using a DC motor model.