\(H^{\infty}\) control for fuzzy singularly perturbed systems. (English) Zbl 1140.93356
Summary: Both the state feedback and static output feedback \(H^{\infty}\) controllers for fuzzy singularly perturbed systems are investigated. We give sufficient conditions for the existence of \(H^{\infty}\) controller such that the closed-loop fuzzy control system is globally stable and achieves a prescribed level of disturbance attenuation for sufficiently small perturbation parameters. The linear matrix inequality (LMI) approach is proposed to obtain the state-feedback gains, and a homotopy-based iterative LMI algorithm is developed to get the static output feedback gains. Simulation results for two examples are included to demonstrate the effectiveness of the proposed approaches.
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