H_∞ Control for Interval Type-2 Fuzzy Singularly Perturbed Nonlinear Systems with Markov Jumping Parameters

This paper investigates the control issue for interval type-2 (IT2) fuzzy singularly perturbed systems with Markov jumping parameters. In order to get closer to the practical physical systems, it is feasible to embed IT2 fuzzy logic sets in the singularly perturbed systems. The stochastic parameters and the transition probabilities contained in the systems are generated from the Markov process. Then, the IT2 fuzzy singularly perturbed systems are guaranteed to achieve the stochastic stability with an H_∞ performance by the designed controller. Afterward, some conditions are established to guarantee the stochastic mean-square stable of the system. Finally, the availability of the proposed fuzzy control scheme is verified by a numerical example.