Fuzzy SMC for Discrete Nonlinear Singularly Perturbed Models With Semi-Markovian Switching Parameters

This article investigates the sliding mode control (SMC) issue for discrete nonlinear semi-Markovian switching singularly perturbed models with incomplete semi-Markovian kernels (SMKs). A Takagi–Sugeno fuzzy model is adopted to characterize the underlying model with singularly perturbed parameters, which is more widely used in nonlinear systems. Because the statistical characteristic of a semi-Markovian kernel is laborious to be obtained in practical engineering, the information of a semi-Markov kernel is recognized to be incomplete. The main novelty lies in constructing a suitable fuzzy SMC scheme to realize the attainment of the quasi-sliding mode, overcoming the difficulty caused by an incomplete SMK. Based on the Lyapunov function related to the fuzzy rule and the elapsed time of current mode, the stability criterion is constructed for the corresponding model. An appropriate SMC approach is then developed to achieve the attainment of a quasi-sliding mode. Finally, the theoretical results are verified by an improved tunnel diode circuit model.