Relaxed LMI based designs for Takagi Sugeno fuzzy regulators and observers poly-quadratic lyapunov function approach

This paper addresses the analysis and design of the state and output feedback fuzzy control for the stabilization of the closed loop continuous time Takagi-Sugeno fuzzy system. The approach utilized in this paper is the so called poly Lyapunov function or fuzzy Lyapunov function. An ordinary parallel distributed compensation design technique is used for the state feedback and the output feedback stabilization control problems. Sufficient conditions for both cases in terms of linear matrix inequality are derived. The proposed design procedure subjected to fuzzy Lyapunov function cures the limitation of the previous results in dealing with the time derivative of premise membership functions and use the natural PDC control. The derived stability condition is more relaxed than the previous results. Moreover, the regulator and observer based stabilization problems are cast as a linear matrix inequality feasibility problem instead of the conventional bilinear matrix inequality. This problem is amenable to solve in the framework of the convex optimization. Finally, a simulation example demonstrates the advantage of the given technique.