时变时滞不确定离散Markov跳跃广义系统的鲁棒输出反馈镇定  

Robust stabilization for uncertain discrete-time Markov jump descriptor systems with time-varying delays via output feedback controllers

作　　者：张华平[1,2] 马树萍[3] 范洪达[1] 

机构地区：[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]山东大学数学学院,山东济南250100

出　　处：《山东大学学报（理学版）》2012年第1期62-71,76,共11页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(61074037)

摘　　要：考虑了时滞不确定离散Markov跳跃线性广义系统的鲁棒稳定性和动态输出反馈镇定问题,时滞是时变的且不确定是范数有界的参数不确定。对所讨论的广义系统进行受限系统等价变换,然后引进新的状态变量,将原有系统等价转换为时滞Markov跳跃标准线性系统。通过构建一个新颖的Lyapunov-Krasovskii函数,得到了判定系统正则、因果和鲁棒随机稳定的线性矩阵不等式(linear matrix inequality,LMI)的充分条件。对于转移概率已知和未知但是具有上界的情形,分别给出了动态输出反馈控制器的设计方法。最后,数值算例验证了本文方法的有效性。The problems of robust stability and robust stabilization via dynamic output feedback for uncertain discrete- time Markov jump descriptor systems with time-varying delays are discussed, where the uncertain is the norm-bounded parameter uncertainty and the delays are time-varying. Based on the restricted system equivalent （ r. s. e. ） transforma- tion and by introducing new state vectors, the discussed system is transformed into a discrete-time Markov jump stand- ard linear system. Then the transformed system is discussed. By constructing a novel Lyapunov-Krasovskii functional, a sufficient condition for the system to be regular, causal and robust stochastically stable is established in terms of linear matrix inequalities （LMIs）. And the dynamic output feedback controllers with full and partial knowledge of transition probabilities are obtained, respectively. Finally, a numerical example is given to illustrate the effectiveness of the pro- posed method.

关 键 词：离散Markov跳跃广义系统 时变时滞 输出反馈 线性矩阵不等式(LMI) 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]