一类不确定非线性离散时滞系统的鲁棒H∞滤波设计

考虑一类同时带有非线性动态和参数不确定性的离散时滞系统的鲁棒H∞滤波设计问题．假设参数不确定性具有线性分式形式,而非线性动态满足Lipschitz条件,给出滤波器使误差系统鲁棒渐近稳定且达到指定的干扰抑制水平．对参数已知情形,先建立广义有界实引理,然后给出H∞滤波器的存在条件,证明了H∞滤波器的存在性可归结为线性矩阵不等式的可解性,基于线性矩阵不等式给出了H∞滤波器的综合方法和步骤．对参数不确定性情形,通过引进标度参数,将不确定非线性离散时滞系统的鲁棒H∞滤波问题转化为确定系统的H∞滤波设计．最后给出仿真例子验证所得结果的有效性．

Robust H-infinity filtering for a class of nonlinear discrete time-delay systems with parameter uncertainties

Robust H-infinity filtering for a class of nonlinear discrete time-delay systems with parameter uncertainties is considered. The uncertainties are in a fractional form and the nonlinearities satisfy Lipschitz condition. The objective is the design of a full-order filer which guarantees not only the robust asymptotic-stability but also a prescribed disturbance attenuation level for the error system, irrespective of the parameter uncertainties. For systems without parameter uncertainties, a generalized bounded real lemma is first introduced, then sufficient conditions for the existence of H-infinity filters are derived. It is shown that the existence of H-infinity filters can be reduced to the solvability of linear matrix inequalities. Methods of designing H-infinity filters are provided in a framework of linear matrix inequalities. As for uncertain systems, the robust H-infinity filtering problem can be solved in terms of a scaled H-infinity filtering problem without uncertainties. Finally a numerical example is given to illustrate the effectiveness of the obtained results.