Stabilization Control with Optimal L₁-Gain and L_∞-Gain for Positive T-S Fuzzy Systems

In this paper, the problem of stabilization with optimal L1-gain for positive T-S fuzzy systems is investigated with the use of linear Lyapunov function. A T-S fuzzy model for positive nonlinear system is established to study the stabilization control for the positive system. Sufficient condition for stabilization is presented in term of linear programming. The static output-feedback fuzzy controller is constructed to guarantee that the closed-loop system is controlled positive, asymptotically stable and the L1-gains from the exogenous inputs to the regulated output is minimized, respectively. Moreover, the stabilization problem with optimal L∞-gain for positive T-S fuzzy systems is solved. Finally, three examples are presented to show the effectiveness of the theoretical results.