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带有多胞型摄动的线性切换系统的二次稳定性

Quadratic stability of switched linear systems with polytopic perturbations
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摘要 研究了带有多胞型摄动的线性切换系统的二次稳定性问题。这种摄动是由若干已知常数矩阵所张成的多胞构成的。利用完备性给出二次稳定的充要条件和切换律的设计方法,利用凸组合技术给出了二次稳定的一个充分条件。这些方法能够分析含有不稳定子系统的多胞型切换系统的稳定性。仿真例子说明了文中结果的正确性。 This paper investigates the quadratic stability problem of switched linear systems with polytopic perturbations. The perturbations form a polytopic spanned by a number of constant known matrixes. Using the concept of completeness, a sufficient and necessary condition that guarantees quadratic stability is given with a switching law. A sufficient condition for quadratic stability is also given via convex combination method. This method can be used to analyze the stability of switched linear systems which has unstable subsystems with polytopic perturbations. The simulation example shows the correctness of the results.
作者 孙文安 赵军
机构地区 东北大学信息科学与工程学院
出处 《电机与控制学报》 EI CSCD 北大核心 2005年第2期103-105,110,共4页 Electric Machines and Control
基金 国家自然科学基金(60274009) 高等学校博士学科点专项科研基金(20020145007) 辽宁省自然科学基金(20032020)
关键词 线性切换系统 稳定性 胞型摄动 控制函数 滑模控制理论 switched linear systems polytopic perturbations quadratic stability lyapunov function
分类号 TP13 [自动化与计算机技术—控制理论与控制工程] O231 [理学—运筹学与控制论]
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参考文献12

  • 1LIBERZON D, MORSE A S. Basic problems in stability and design of switched systems[J]. IEEE Control System Magazine. 1999, 19(1) : 59 -70.
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二级参考文献24

  • 1[1]Liberzon D, Morse A S. Basic problems in stability and design of switched systems[J]. IEEE Control System Magazine, 1999,19(5):59-70.
  • 2[2]Decarlo R A, Branicky M S. Perspectives and results on the stability and stabilizability of hybrid system[J]. Proceedings of the IEEE, 2000,88(7):1069-1082.
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  • 6[7]Shorter R, Narendra K S, Mason O. A result on common quadratic Lyapunov functions[J]. IEEE Transitions on Automatic Control, 2003,48(1):110-113.
  • 7[8]Hu B, Zhai G, Miche A N. Common quadratic Lyapunov-like functions with associated switching regions for two unstable second-order LTI systems[J]. INT J Control, 2002,75(14):1127-1135.
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  • 10[11]Xie D. Wang L. Robust stability analysis and control synthesis for discrete-time uncertain switched systems[A]. Proceedings of the 42nd IEEE Conference on Decision and Control[C]. Maui, 2003.4812-4817.

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电机与控制学报
2005年 第2期

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