Robust Filtering for Nonlinear Nonhomogeneous Markov Jump Systems by Fuzzy Approximation Approach

This paper addresses the problem of robust fuzzy L2 - L∞ filtering for a class of uncertain nonlinear discrete-time Markov jump systems (MJSs) with nonhomogeneous jump processes. The Takagi-Sugeno fuzzy model is employed to represent such nonlinear nonhomogeneous MJS with norm-bounded parameter uncertainties. In order to decrease conservation, a polytope Lyapunov function which evolves as a convex function is employed, and then, under the designed mode-dependent and variation-dependent fuzzy filter which includes the membership functions, a sufficient condition is presented to ensure that the filtering error dynamic system is stochastically stable and that it has a prescribed L2 - L∞ performance index. Two simulated examples are given to demonstrate the effectiveness and advantages of the proposed techniques.

本文研究了一类具有非齐次跳变过程的不确定非线性离散时间马尔可夫跳变系统（MJSs）的鲁棒模糊L2 - L∞滤波问题。采用Takagi - Sugeno模糊模型来表示这种具有范数有界参数不确定性的非线性非齐次MJS。为了减少保守性，采用了一种作为凸函数演化的多面体李雅普诺夫函数，然后，在设计的包含隶属函数的模式相关和变化相关的模糊滤波器下，给出了一个充分条件，以确保滤波误差动态系统是随机稳定的，并且具有规定的L2 - L∞性能指标。给出了两个仿真例子来证明所提出技术的有效性和优势。