SMC for Discrete Semi-Markov Switching Slow Sampling Singularly Perturbed Models With Applications
Wenhai Qi, Ning Zhang, Guangdeng Zong, Choon Ki Ahn
Abstract
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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> -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.