Dynamic Output Feedback Control for Continuous-Time T–S Fuzzy Systems Using Fuzzy Lyapunov Functions

A novel relaxation approach is proposed for the analysis and dynamic output feedback control of continuous-time Takagi–Sugeno (T–S) fuzzy systems using fuzzy Lyapunov functions. Previous relaxation methods for T–S fuzzy systems have some drawbacks in relaxing quadratic functions depending on normalized fuzzy weighting functions. They often introduce conservatism or lead to computational difficulty in analysis and control synthesis. Different from previous works, the proposed approach employs linear fractional transformation mechanism and full-block
$S$
-procedure to reduce the conservatism in analysis. Furthermore, the relaxation technique proposed in this paper can be used in solving the controller synthesis problem effectively. As a result, a design procedure of a nonparallel distributed compensation output feedback controller, which ensures asymptotic stability and optimizes
${\mathcal L}_2$
gain performance of the closed-loop systems, is provided. Several examples have been used to illustrate the advantages and efficiency of the proposed method extensively.