Title :
Robust H∞ control for fuzzy systems with Frobenius norm-bounded uncertainties
Author :
Lo, Ji-Chang ; Lin, Min-Long
Author_Institution :
Fac. of Mech. Eng., Nat. Central Univ., Chung-li, Taiwan
Abstract :
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.
Keywords :
H∞ control; Lyapunov methods; continuous time systems; control system synthesis; discrete time systems; fuzzy control; linear matrix inequalities; linear systems; robust control; state feedback; uncertain systems; Frobenius norm-bounded uncertainties; Lyapunov method; bounded real lemma; continuous system; controller synthesis; discrete-time system; linear matrix inequality; linear theory; matrix algebra; robust H∞ control; stabilization; state feedback fuzzy control; uncertain fuzzy systems; Fuzzy systems; Linear feedback control systems; Lyapunov method; Matrices; Robust control; Robustness; State feedback; Sufficient conditions; Uncertain systems; Uncertainty; Bounded real lemma; Frobenius norm; Takagi–Sugeno (T–S) fuzzy model; linear matrix inequality (LMI);
Journal_Title :
Fuzzy Systems, IEEE Transactions on
DOI :
10.1109/TFUZZ.2005.861602
