Further relaxed stability conditions for continuous-time polynomial fuzzy system based on polynomial fuzzy Lyapunov function

This paper concerns a new stability condition for polynomial fuzzy system by introducing polynomial fuzzy Lyapunov function and slack matrix. Stability condition for polynomial fuzzy system is usually derived by common quadratic polynomial Lyapunov function. However this method results the conservative problem. To relax the conservative result, various relaxing methods which are introduced in T-S fuzzy system case are converted to polynomial fuzzy system. With this line, this paper adapts fuzzy Lyapunov function and extends it to polynomial fuzzy Lyapunov function. It is the extended version of existing fuzzy Lyapunov function which is replaced constant matrices with polynomial one. Furthermore, by adding the slack matrix to the proposed stability condition, this condition is further relaxed. Finally, these results will be proved by numerical example.