This paper determines the designing of a non-fragile H ∞ output feedback controller for a class of nonlinear uncertain dynamical systems with multiple timescales described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop a non-fragile H ∞ output feedback controller which guarantees the L 2 -gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value for this class of uncertain fuzzy dynamical

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... systems with multiple time-scales. A numerical example is provided to illustrate the design developed in this paper. A Non-Fragile H ∞ Output Feedback Controller for Uncertain Fuzzy Dynamical Systems with Multiple Time-Scales 9 design that guarantees closed-loop stability and performance. Recently, a great amount of effort has been devoted to describing a nonlinear system using a Takagi-Sugeno fuzzy model; see [16]-[29]. The Takagi-sugeno (TS) fuzzy model represents a nonlinear system by a family of local linear models which smoothly blended together through fuzzy membership functions. Unlike conventional modelling techniques which uses a single model to describe the global behavior of a nonlinear system, fuzzy modelling is essentially a multi-model approach in which simple sub-models (typically linear models) are fuzzily combined to described the global behavior of a nonlinear system. Based on this fuzzy model, a number of systematic model-based fuzzy control design methodologies have been developed. The aim of this paper is to design a non-fragile H ∞ output feedback controller for a uncertain nonlinear dynamical system with multuple time-scales. Based on an LMI approach, we develop the fuzzy non-fragile H ∞ output feedback controller that guarantees the L 2 -gain of the mapping from the exogenous input noise to the regulated output to be less than or equal to a prescribed value for this class of fuzzy dynamical systems. In order to alleviate the ill-conditioned linear matrix inequalities resulting from the interaction of slow and fast dynamic modes, the illconditioned LMIs are decomposed into ε-independent and ε-dependent LMIs. The ε-independent LMIs are not ill-conditioned and the ε-dependent LMIs tend to zero when ε approaches to zero. It can be shown that when ε is sufficiently small, the original ill-conditioned LMIs are solvable if and only if the ε-independent LMIs are solvable. The proposed approach does not involve the separation of states into slow and fast ones, and it can be applied not only to standard, but also to nonstandard singularly perturbed systems. This paper is organized as follows. In Section 2, system descriptions and definition are presented. In Section 3, based on an LMI approach, we respectively develop a technique for designing a non-fragile H ∞ output feedback controllers such that the L 2 -gain of the mapping from the exogenous input noise to the regulated output is less than a prescribed value for the system described in Section 2. The validity of this approach is demonstrated by an example from a literature in Section 4. Finally, conclusions are given in Section 5.