Composite Fuzzy Control of Nonlinear Singularly Perturbed Systems

Author

Li, Tzuu-Hseng S. ; Lin, Kuo-Jung

Author_Institution

Dept. of Electr. Eng., Nat. Cheng Kung Univ., Tainan

Volume

15

Issue

2

fYear

2007

fDate

4/1/2007 12:00:00 AM

Firstpage

176

Lastpage

187

Abstract

This paper presents the composite fuzzy control to stabilize the nonlinear singularly perturbed (NSP) systems with guaranteed H^infin control performance. We use the Takagi-Sugeno (T-S) fuzzy model to construct the singularly perturbed fuzzy (SPF) systems. The corresponding fuzzy slow and fast subsystems of the original SPF system are also obtained. At first, a set of common positive-define matrices and the controller gains are determined by the Lyapunov stability theorem and linear matrix inequality (LMI) approach. Then, a sufficient condition is derived for the robust stabilization of NSP systems. The composite fuzzy control will stabilize the original NSP systems for all epsivisin(0,epsiv^*) and the allowable perturbation bound epsiv^* can be determined via some algebra inequalities. A practice example is adopted to demonstrate the feasibility and effectiveness of the proposed control scheme

Keywords

H^infin control; Lyapunov methods; fuzzy control; linear matrix inequalities; nonlinear control systems; singularly perturbed systems; stability; Lyapunov stability theorem; Takagi-Sugeno fuzzy model; composite fuzzy control; guaranteed H^infin control; linear matrix inequality; nonlinear singularly perturbed system stability; positive-define matrices; robust stabilization; Algebra; Control systems; Fuzzy control; Fuzzy systems; Linear matrix inequalities; Lyapunov method; Nonlinear control systems; Robustness; Sufficient conditions; Takagi-Sugeno model; $H^{infty}$ control performance; Takagi-Sugeno (T-S) fuzzy model; linear matrix inequality (LMI); nonlinear singularly perturbed (NSP) systems; singularly perturbed fuzzy (SPF) systems;

fLanguage

English

Journal_Title

Fuzzy Systems, IEEE Transactions on

Publisher

ieee

ISSN

1063-6706

Type

jour

DOI

10.1109/TFUZZ.2006.878252

Filename

4142757