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.

中文翻译：

---

$H_{\infty }$ 广义Lyapunov函数并引入外部变量的连续时间Takagi–Sugeno模糊模型控制

对于模糊系统，已知隶属函数依赖的李雅普诺夫函数可以减少由二次李雅普诺夫函数产生的保守性，但是隶属函数的时间导数很难处理。在本技术论文中，设计了一种广义Lyapunov函数（称为齐次多项式隶属函数Lyapunov函数），并提出了相应的HPMFD切换来处理隶属函数的时间导数。另外，构造了广义外部变量以进一步改善结果。最后的例子说明了该方法的有效性。