变时滞不确定广义Markovian跳系统的滑模控制

doi:10.6040/j.issn.1672-3961.0.2013.309

山东大学学报(工学版) ›› 2014, Vol. 44 ›› Issue (4): 31-38.doi: 10.6040/j.issn.1672-3961.0.2013.309

变时滞不确定广义Markovian跳系统的滑模控制

解静¹, 考永贵², 高存臣³, 张孟乔²

1. 中国海洋大学信息科学与工程学院, 山东青岛 266100;
2. 哈尔滨工业大学理学院数学系, 山东威海 264209;
3. 中国海洋大学数学科学学院, 山东青岛 266100

收稿日期:2013-10-30 修回日期:2014-05-30 发布日期:2013-10-30
作者简介:解静（1987-），女，山东泰安人，博士研究生，主要研究方向为随机控制系统的理论及应用.E-mail：tiantian1210x@163.com
基金资助:
国家高技术研究发展计划（863计划）资助项目（2008 AA04Z401，2009AA043404）；教育部重点科研基金资助项目（NCET-08-0755）

Integral sliding mode control for uncertain stochastic singular Markovian jump systems with time-varying delays

XIE Jing¹, KAO Yonggui², GAO Cunchen³, ZHANG Mengqiao²

1. College of Information Science and Engineering, Ocean University of China, Qingdao 266100, Shandong, China;
2. Department of Mathematics, Harbin Institute of Technology, Weihai 264209, Shandong, China;
3. School of Mathematical Sciences, Ocean University of China, Qingdao 266100, Shandong, China

Received:2013-10-30 Revised:2014-05-30 Published:2013-10-30

摘要/Abstract

摘要： 针对一类含有变时滞和非匹配不确定参数的随机广义Markovian跳系统，提出一种滑模控制的方案。首先构造不带跳变的切换函数，利用线性矩阵不等式给出该系统随机鲁棒渐近稳定的充分条件；然后，为使闭环系统的状态轨迹在有限时间内到达切换面，利用Lyapunov稳定性方法设计了滑模控制器及切换规则；最终使闭环系统产生稳定的滑动模态。数值算例验证了该方法的有效性和可行性。

关键词: 随机广义Markovian跳系统, 变时滞, 不确定参数, 随机鲁棒渐近稳定, 滑模控制器

Abstract: A sliding mode control scheme was proposed for a class of stochastic singular Markovian jump systems with time-varying delays and mismatched uncertain parameters. A switching function without Markovian jump were constructed at first, and a sufficient condition of the stochastically robust asymptotic stability was obtained for the system in terms of linear matrix inequalities(LMIs). Secondly, sliding mode controllers and switching laws are designed by the Lyapunov stability method to make state trajectories of the closed-loop system reach switching surfaces in finite time. Finally, the stable sliding mode dynamics was resulted for the closed-loop system. The proposed scheme was testified to be effective and feasible by a numerical example.

Key words: stochastic singular Markovian jump system, stochastically robust asymptotic stability, time-varying delay, sliding mode controller, uncertain parameter

中图分类号:

TP271

解静, 考永贵, 高存臣, 张孟乔. 变时滞不确定广义Markovian跳系统的滑模控制[J]. 山东大学学报(工学版), 2014, 44(4): 31-38.

XIE Jing, KAO Yonggui, GAO Cunchen, ZHANG Mengqiao. Integral sliding mode control for uncertain stochastic singular Markovian jump systems with time-varying delays[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2014, 44(4): 31-38.

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变时滞不确定广义Markovian跳系统的滑模控制

Integral sliding mode control for uncertain stochastic singular Markovian jump systems with time-varying delays

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