Robust ℋ∞ filtering of Markovian jump stochastic systems with uncertain transition probabilities
Robust ℋ∞ filtering of Markovian jump stochastic systems with uncertain transition probabilities
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DOI：
10.1080/00207720903513350
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发表时间：
2011-07
影响因子：
4.3
通讯作者：
Xiu-ming Yao;Ligang Wu;W. Zheng;Changhong Wang
中科院分区：
文献类型：
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作者：
Xiu-ming Yao;Ligang Wu;W. Zheng;Changhong Wang
研究了一类不确定马尔可夫随机系统的鲁棒鲁棒滤波问题。所考虑的系统不仅包含伊藤型随机干扰和时变时滞，而且在系统矩阵和模式转移率矩阵中都包含不确定性.我们的目标是设计一个滤波器，使得对于所有允许的参数不确定性和时滞，滤波误差系统都是鲁棒随机稳定的，并达到一个给定的干扰抑制衰减水平。通过构造一个适当的随机Lyapunov-Krasovskii泛函和采用自由权矩阵技术，所需的过滤器的存在的充分条件，建立在线性矩阵不等式，这可以很容易地解决了标准的数值软件。最后，一个数值例子来显示所开发的方法的实用性。
This article investigates the problem of robust ℋ∞ filtering for a class of uncertain Markovian stochastic systems. The system under consideration not only contains Itô-type stochastic disturbances and time-varying delays, but also involves uncertainties both in the system matrices and in the mode transition rate matrix. Our aim is to design an ℋ∞ filter such that, for all admissible parameter uncertainties and time-delays, the filtering error system can be guaranteed to be robustly stochastically stable, and achieve a prescribed ℋ∞ disturbance rejection attenuation level. By constructing a proper stochastic Lyapunov–Krasovskii functional and employing the free-weighting matrix technique, sufficient conditions for the existence of the desired filters are established in terms of linear matrix inequalities, which can be readily solved by standard numerical software. Finally, a numerical example is provided to show the utility of the developed approaches.