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.
- Bounded real lemma
- Frobenius norm
- H control
- Linear matrix inequality (LMI)
- Takagi-Sugeno (T-S) fuzzy model