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一类切换时滞奇异系统的状态反馈H控制付主木 吴庆涛 费树岷


  摘 要:研究一类由任意有限多个时滞奇异子系统组成的切换系统的状态反馈H∞控制问题。利用Lyapunov函数方法和凸组合技术,给出由矩阵不等式表示的控制器存在的充分条件,并设计了相应的子控制器和切换规则。采用变量替代方法,将该矩阵不等式转换为一组线性矩阵不等式(LMIs),最后给出一个求解状态反馈控制器增益矩阵的仿真算例。研究结果表明,通过切换,闭环系统在整个状态空间上的每个点都满足H∞性能,并不要求每个子系统在整个状态空间上都满足H∞性能,甚至也不要求其渐进稳定。

  关键词:切换系统;奇异系统;H∞控制;状态反馈;状态时滞;线性矩阵不等式

  中图分类号:TP273 文献标志码:A

   文章编号:1001-3695(2008)07-2013-03

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  State feedback H∞ control for class of switched singular systems with state delay

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  FU Zhumu1,WU Qingtao1,FEI Shumin2

  (1.School of Electronic Information Engineering, Henan University of Science & Technology, Luoyang Henan 471003, China;2.School of Automation, Southeast University, Nanjing 210096, China)

  Abstract:It is investigated that state feedback H∞ control problem for a class of switched singular systems with state delay.Based on Lyapunov function approaches and convex combinations techniques, a sufficient condition for the existence of subcontrollers was presented, which was in the form of matrix inequalities. Both subcontrollers and switching strategy were designed. Then, using variable substitution method, the matrix inequalities were changed into linear matrix inequalities (LMIs). Finally, a simulation example was given to solve the gain matrices of state feedback controllers. The results indicate that closed loop system satisfies H∞ performance at each point in whole statespace through switching, although each subsystem doesn’t satisfy the performance and even is not asymptotically stable.

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