Novel SMC for Discrete Nonhomogeneous Semi-Markov Switching Systems With Application to DC–DC Buck Converter Circuit

This paper investigates a novel learning-based sliding mode control (SMC) strategy for a class of nonhomogeneous semi-Markov switching systems with incomplete sojourn-time information. In contrast to existing studies, the sojourn-time probability density functions of semi-Markov kernel are considered to be incompletely known, relaxing the assumption of completely known sojourn-time distributions. The main novelty lies in constructing a novel learning-based SMC scheme to realize the attainment of the quasi-sliding mode, overcoming the difficulty caused by incomplete sojourn-time information. By utilizing the upper bounds of sojourn time for each subsystem mode and constructing the multiple-Lyapunov function, sufficient conditions for mean-square stability are derived for the resulting closed-loop system. Moreover, a recursive sliding mode learning controller is developed to ensure finite-time reachability of the sliding motion and to effectively suppress both parametric uncertainties and switching-induced chattering. The effectiveness and practical applicability of the proposed method are validated through the DC-DC buck converter application.