Interval type-2 fuzzy H∞ filtering for nonlinear singularly perturbed jumping systems: A semi-Markov kernel method

Abstract

This paper addresses the $H_{\infty }$ filtering issue for nonlinear singularly perturbed jump systems with semi-Markov process. The interval type-2 fuzzy model is employed to handle the uncertain features and nonlinearity inherent in the considered systems. Designing an interval type-2 fuzzy filter, it is related to the system mode but remains independent of the singular perturbation parameter, this approach utilizes the semi-Markov kernel method and non-parallel distributed compensation technique. Some criteria with incorporating the message of membership functions are derived to ensure that the filtering error system is mean-square exponentially stable while meeting specified $H_{\infty }$ performance. Introduction of slack matrices with two adjustable scalars facilitates obtaining the interval type-2 fuzzy filter gains. The rationality of the proposed approach is demonstrated through the utilization of two examples, including a circuit model.