H∞ control for continuous-time Takagi–Sugeno fuzzy model by applying generalized Lyapunov function and introducing outer variables

Abstract For fuzzy systems, it is known that membership function dependent Lyapunov function can reduce the conservatism that has arisen from quadratic Lyapunov function but the time derivative of membership function is hard to be dealt with. In this technical paper, a kind of generalized Lyapunov function (called homogeneous polynomially membership functions dependent (HPMFD) Lyapunov function ) is designed and the corresponding HPMFD switching is proposed to deal with the time derivative of membership function. In addition, the generalized outer variable is constructed to further improve the results. The final example shows the effectiveness of the proposed method.