Robust H∞H∞ fuzzy filter design for uncertain nonlinear singularly perturbed systems with Markovian jumps: An LMI approach

This paper examines the problem of designing a robust H∞H∞ fuzzy filter for a singularly perturbed Takagi–Sugeno (TS) fuzzy system with Markovian jumps. Based on a linear matrix inequality (LMI) approach, sufficient conditions for the existence of a robust H∞H∞ fuzzy filter are derived in terms of a family of LMIs. To alleviate the numerical stiffness resulting from the interaction of slow and fast dynamic modes, solutions to the problem are given in terms of linear matrix inequalities which are independent of the singular perturbation ε. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied to both standard and nonstandard nonlinear singularly perturbed systems. A numerical example is provided to illustrate the design developed in this paper.