This article is concerned with the problems of extended dissipativity analysis and filter design for interval type-2 (IT2) fuzzy systems. Based on the line integral Lyapunov function, a sufficient condition of asymptotic stability and extended dissipativity of the systems under consideration is established. A LMI-based equivalent condition to the obtained one in a nonlinear form is provided by combining congruence transformation with change of variables. This LMI condition obtained is more general than the one which is based on the common quadratic Lyapunov function. Meanwhile, in terms of parameterization, the extended dissipative filter is developed which guarantees the asymptotic stability and extended dissipativity for the filtering error system. Furthermore, our filter obtained by the parameterization method includes the one obtained by the equivalent transformation method as a special case. Two simulation examples are provided to show the merits and effectiveness of the proposed approach.

中文翻译：

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区间2型模糊系统扩展耗散滤波的线积分法


本文关注区间类型 2 (IT2) 模糊系统的扩展耗散分析和滤波器设计问题。基于线积分李亚普诺夫函数，建立了所考虑系统渐近稳定性和扩展耗散性的充分条件。通过将同余变换与变量变化相结合，提供了一种基于 LMI 的非线性形式的等价条件。所获得的 LMI 条件比基于常见二次 Lyapunov 函数的 LMI 条件更通用。同时，在参数化方面，提出了扩展耗散滤波器，保证了滤波误差系统的渐近稳定性和扩展耗散性。此外，我们通过参数化方法获得的滤波器包括通过等效变换方法获得的滤波器作为一种特例。提供了两个仿真示例来展示所提出方法的优点和有效性。