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

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. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This technical paper introduces a generalized Lyapunov function called HPMFD and proposes a corresponding switching method to deal with the time derivative of membership function. By constructing a generalized outer variable, the results are further improved. The effectiveness of the proposed method is demonstrated in a final example.