SMC for Discrete Semi-Markov Switching Slow Sampling Singularly Perturbed Models With Applications

The sliding mode control (SMC) is addressed for discrete-time semi-Markov switching slow sampling singularly perturbed models. Under only the part known semi-Markov kernel, the $\varepsilon$ -dependent sliding function is designed for the underlying system. Based on the upper bound of the sojourn time of each system mode, sufficient conditions are obtained for mean-square stability. Then, a strategy to estimate the upper bound of the singularly perturbed parameter is given under an incomplete semi-Markov kernel. Moreover, an appropriate SMC scheme is synthesized to drive the system states onto the pre-specified sliding region. An inverted pendulum model is adopted to verify the practicability of the proposed strategy.