H∞ Output Feedback Control Design for Uncertain Fuzzy Systems with Multiple Time Scales: An LMI Approach

This paper examines the problem of designing a robust H∞ output feedback controller for an uncertain Takagi-Sugeno (TS) fuzzy system with multiple time scales. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain TS fuzzy system with multiple time scales to have an H∞ performance are derived. To eliminate the numerical stiffness caused by the interaction of slow and fast dynamic modes, solutions to the problem are presented in terms of LMIs which are independent of the singular perturbation ε. The proposed approach does not involve the separation of states into slow and fast and it can be applied not only to standard, but also to nonstandard singularly perturbed nonlinear systems. A numerical example is provided to illustrate the design techniques developed in this paper.