Static-Output-Feedback ${mathscr H}_{bm infty }$ Control of Continuous-Time T–S Fuzzy Affine Systems Via Piecewise Lyapunov Functions

摘要

This paper investigates the problem of robust ${mathscr H}_{infty }$ output feedback control for a class of continuous-time Takagi–Sugeno (T–S) fuzzy affine dynamic systems with parametric uncertainties and input constraints. The objective is to design a suitable constrained piecewise affine static output feedback controller, guaranteeing the asymptotic stability of the resulting closed-loop fuzzy control system with a prescribed ${mathscr H}_{infty }$ disturbance attenuation level. Based on a smooth piecewise quadratic Lyapunov function combined with S-procedure and some matrix inequality convexification techniques, some new results are developed for static output feedback controller synthesis of the underlying continuous-time T–S fuzzy affine systems. It is shown that the controller gains can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, three examples are provided to illustrate the effectiveness of the proposed methods.