Robust H(infinity) control for fuzzy systems with Frobenius norm-bounded uncertainties
In this paper, we investigate the problem of robust H(infinity) 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(infinity) control where necessary and sufficient conditions were obtained, only sufficient condition based on Lyapunov method is shown. Furthermore, connection between robust H(infinity) problems involving uncertainty and standard uncertainly-free H(infinity) 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.
h(infinity) control bounded real lemma linear matrix inequality (lmi) frobenius norm takagi-sugeno (t-s) fuzzy model