L2 − L∞ filtering for Markovian jump systems with time-varying delays and partly unknown transition probabilities
L2 − L∞ filtering for Markovian jump systems with time-varying delays and partly unknown transition probabilities
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DOI：
10.1016/j.cnsns.2011.11.033
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发表时间：
2012-07
影响因子：
3.9
通讯作者：
Yucai Ding;Hong Zhu;S. Zhong;Yuping Zhang
中科院分区：
文献类型：
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作者：
Yucai Ding;Hong Zhu;S. Zhong;Yuping Zhang
本文研究了马尔可夫跳变系统的L2−L∞滤波问题。所考虑的系统包含时变时滞、扰动信号和部分未知的转移概率。本文的目的是设计一个滤波器，它适用于精确已知和部分未知的转移概率，使得滤波误差系统是随机稳定的，并保证一个指定的L2−L∞干扰衰减水平。利用Lyapunov-Krasovskii泛函，给出了线性矩阵不等式形式的充分条件.数值例子说明了所提出的主要结果的有效性。这些结果可望对转移概率部分未知的马尔可夫跳变系统的滤波器设计研究有所帮助。
This paper considers the L2−L∞filtering problem for Markovian jump systems. The systems under consideration involve time-varying delays, disturbance signal and partly unknown transition probabilities. The aim of this paper is to design a filter, which is suitable for exactly known and partly unknown transition probabilities, such that the filtering error system is stochastically stable and a prescribed L2−L∞disturbance attenuation level is guaranteed. By using the Lyapunov–Krasovskii functional, sufficient conditions are formulated in terms of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed main results. All these results are expected to be of use in the study of filter design for Markovian jump systems with partly unknown transition probabilities.