[1]张端金,王钟堃.具有丢包的未知转移概率 Markov 跳变系统鲁棒 H∞ 滤波[J].郑州大学学报(工学版),2021,42(6):1-7.[doi:10.13705/j.issn.1671-6833.2021.04.007]
　Zhang Duanjin,Wang Zhongkun,Robust H∞ Filtering for Markov Jump Systems with Unknown Transition Probabilities and Packet Dropouts[J].Journal of Zhengzhou University (Engineering Science),2021,42(6):1-7.[doi:10.13705/j.issn.1671-6833.2021.04.007]
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具有丢包的未知转移概率 Markov 跳变系统鲁棒 H∞ 滤波
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《郑州大学学报(工学版)》[ISSN:1671-6833/CN:41-1339/T]

卷:
42
期数:
2021年6期
页码:
1-7
栏目:
出版日期:
2021-11-10

文章信息/Info

Title:
Robust H∞ Filtering for Markov Jump Systems with Unknown Transition Probabilities and Packet Dropouts
作者:
张端金,王钟堃
郑州大学 信息工程学院，河南 郑州 450001

Author(s):
Zhang Duanjin; Wang Zhongkun;
School of Information Engineering, Zhengzhou University, Zhengzhou 450001, China
关键词:
Keywords:
Markov jumping systems;  uncertain parameters;  packet dropouts;  Delta operator
DOI:
10.13705/j.issn.1671-6833.2021.04.007
文献标志码:
A
摘要:
研究一类具有数据包丢失的部分未知转移概率离散时间马尔可夫跳变系统( MJSs) 鲁棒 H∞ 滤波问题。假定系统丢包发生在传感器至滤波器之间的通信信道且丢包概率服从伯努利分布，基于 Delta算子离散化方法构造具有不确定参数的离散时间马尔可夫跳变系统及模态相关的全阶滤波器。引入松弛矩阵变量解决系统矩阵与 Lyapunov 函数中正定矩阵之间的耦合问题。利用 Lyapunov 函数、Schur 补引理及线性矩阵不等式方法获得系统随机稳定且满足 H∞ 性能的充分条件。已知系统丢包率，分别求得Delta 算子系统及移位算子系统最优 H∞ 性能指标。当丢包概率取值越低时系统的鲁棒性能越好，并且在相同丢包概率下，Delta 算子系统最优 H∞ 性能总是优于移位算子系统最优 H∞ 性能。数值仿真结果表明所提方法不仅有效可行，还具有一定的优越性。
Abstract:
The robust H∞filtering problem of Markov jump systems with partly unknown transition probabilities and packet dropouts was investigated. Assuming that the probability of packet dropouts would obey Bernoulli distribution, a discrete-time Markov jump system with uncertain parameters and mode-dependent full-order filter were constructed based on the Delta operator. The slack matrix variables were introduced to solve the cross coupling between the system matrices and the Lyapunov positive matrices. The Lyapunov function, Schur complement and linear matrix inequalities were used to obtain sufficient conditions for the system to be stochastically stable and satisfy H∞ performance. The optimal H∞ performance index of the Delta operator system and the shifting operator system were obtained respectively with the known probability of packet dropouts. When the probability of the packet dropouts were lower, the robust performance as well as the optimal H∞ performance of Delta operator system were better than the shift operator system. Numerical simulation proved that the method proposed in this paper not only was effective and feasible, but also had certain advantages.

参考文献/References:

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更新日期/Last Update: 2021-12-16