具有丢包的未知转移概率Markov跳变系统鲁棒H_(∞)滤波  

Robust H_(∞) Filtering for Markov Jump Systems with Unknown Transition Probabilities and Packet Dropouts

作　　者：张端金[1] 王钟堃 ZHANG Duanjin;WANG Zhongkun(School of Information Engineering, Zhengzhou University, Zhengzhou 450001, China)

机构地区：[1]郑州大学信息工程学院,河南郑州450001

出　　处：《郑州大学学报（工学版）》2021年第6期1-6,41,共7页Journal of Zhengzhou University（Engineering Science）

基　　金：国家自然科学基金资助项目(61471323)。

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。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.

关 键 词：马尔可夫跳变系统 不确定参数 数据包丢失 DELTA算子 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]