时变时滞不确定离散奇异切换系统的鲁棒H∞滤波

J4 ›› 2012, Vol. 47 ›› Issue (7): 59-69.

时变时滞不确定离散奇异切换系统的鲁棒H∞滤波

张华平^1,2,张健鹏³,马树萍⁴, 范洪达¹

1. 海军航空工程学院电子信息工程系, 山东烟台 264001; 2. 烟台大学网络与教育技术中心, 山东烟台 264005;
3. 海军航空工程学院研究生管理大队, 山东烟台 264001; 4.山东大学数学学院, 山东济南 250100

收稿日期:2011-05-05 出版日期:2012-07-20 发布日期:2012-09-01
作者简介:张华平(1967- )，男，博士研究生，研究方向为智能控制，网络控制. Email: zhp@ytu.edu.cn
基金资助:
国家自然科学基金资助项目(61074037)

Robust H_∞ filter design for discrete-time singular switched systems with uncertainties and time-varying delays

ZHANG Hua-ping^1,2, ZHANG Jian-peng^3, MA Shu-ping⁴, FAN Hong-da¹

1. Department of Electronic and Information Engineering, Naval Aeronautics and Astronautics University,
Yantai 264001, Shandong, China; 2. Network Center, Yantai University, Yantai 264005, Shandong, China;
3. Graduate Students’ Brigade, Naval Aeronautics and Astronautics University, Yantai 264001, Shandong, China;
4. School of Mathematics, Shandong University, Jinan 250100, Shandong, China

Received:2011-05-05 Online:2012-07-20 Published:2012-09-01

摘要/Abstract

摘要：

研究了含参数不确定的时变时滞离散奇异切换系统的鲁棒H∞滤波问题。利用受限系统等价变换和引进新状态变量,将所讨论的奇异滤波误差系统等价转换为时滞离散标准切换系统。然后构建了一个新颖的Lyapunov—Krasovskii 函数。通过对转换后的系统进行讨论,采用线性矩阵不等式形式得到了判定系统正则、因果和一致渐近稳定的充分条件,以及对所允许的不确定性满足H∞性能的滤波器设计方法。所得到的结果具有较小的保守性。最后,通过数值算例验证了本文方法的有效性。

关键词: H∞滤波;离散奇异切换系统;时变时滞;不确定;线性矩阵不等式(LMI)

Abstract:

The problem of robust H∞ filter design for discrete-time singular switched systems with parametric uncertainties and time-varying delays is discussed. Based on the restricted system equivalent (r.s.e.) transformation and by introducing new state vectors, the singular filtering error system is transformed into a time-delay standard switched system. The transformed system is then discussed by constructing a novel Lyapunov—Krasovskii functional. A sufficient condition for the filtering error system to be regular, causal and uniformly asymptotically stable and to satisfy H∞ performance for all admissible uncertainties is established in terms of linear matrix inequalities (LMIs), and the corresponding filter design is derived. The obtained results are less conservative. A numerical example is given which illustrates the effectiveness of the new theory.

Key words: H∞ filter; discrete-time singular switched system; time-varying delay; uncertain; linear matrix inequality(LMI)

张华平1,2,张健鹏3,马树萍4, 范洪达1. 时变时滞不确定离散奇异切换系统的鲁棒H∞滤波[J]. J4, 2012, 47(7): 59-69.

ZHANG Hua-ping1,2, ZHANG Jian-peng3, MA Shu-ping4, FAN Hong-da1. Robust H_∞ filter design for discrete-time singular switched systems with uncertainties and time-varying delays[J]. J4, 2012, 47(7): 59-69.

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