Non-fragile Fuzzy Control for Nonlinear Fast Sampling Singularly Perturbed Systems Subject to Markov Jumping Parameters

This article investigates the nonfragile extended dissipative control problem for a class of nonlinear fast sampling singularly perturbed systems subject to Markov jumping parameters. Thereinto, the Tagaki–Sugeno fuzzy model is utilized to describe the nonlinear part, and the nonfragile control strategy is employed to handle the gain variations in a controller. Furthermore, we aim to design a fuzzy nonfragile controller, which can ensure that the systems under consideration are stochastically stable as well as extended dissipative. To this end, through constructing a mode-dependent Lyapunov function and applying the convex optimization theory, some sufficient conditions that are independent of the singular perturbation parameter $\epsilon$ are derived. Besides, a set of controller gains is also obtained by solving the aforesaid conditions. Based on the effectiveness of the controller, the technique to obtain the upper bound of the singular perturbation parameter is developed, and an improved system performance related to such an upper bound is achieved. Finally, through a numerical example and an inverted pendulum model example, the superiority and the practicability of this article are verified.