Tracking Control Design for Takagi-Sugeno Fuzzy Systems Based on Membership Function-Dependent L∞ Performance

Abstract

The design of tracking control based on membership function-dependent L ∞ performance for the systems, which are described by the Takagi-Sugeno fuzzy models, is considered. In practice, most Takagi-Sugeno fuzzy systems have such a characteristic that they work on some local subsystems most of the time and on others less time. Taking advantage of this feature, an L ∞ performance index dependent on membership function is proposed, through which better performance may be guaranteed for those local subsystems that work most of the time. By means of the newly defined L ∞ performance index, the measurable premise variables, the estimation of immeasurable premise variables, and the estimation of nonlinear function, an observer-based tracking controller is designed in the form of linear matrix inequalities, which makes full use of the information of measurable premise variables. Finally, an example is provided to verify the effectiveness of the proposed approach. In the simulation, compared with the traditional L ∞ control method, the novel method has better robust tracking performance.INDEX TERMS L ∞ control, Membership function-dependent, Observer-based tracking controller, Takagi-Sugeno fuzzy system.