Robust H∞ control for fuzzy systems with Frobenius norm-bounded uncertainties

In this paper, we investigate the problem of robust H_∞ performance and stabilization for a class of uncertain fuzzy systems with Frobenius norm-bounded parameter uncertainties in all system matrices. Both continuous- and discrete-time uncertain fuzzy systems are considered under a unified treatment called bounded real lemma for fuzzy systems. Unlike the bounded real lemma in the linear theory of robust H_∞ control where necessary and sufficient conditions were obtained, only sufficient condition based on Lyapunov method is shown. Furthermore, connection between robust H_∞ problems involving uncertainty and standard uncertainty-free H_∞ problems is established via matrix algebra. As for controller synthesis, a state feedback fuzzy control law is designed via relaxed linear matrix inequality (LMI) formulations.