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| 二阶线性系统族的共同二次Lyapunov函数 |
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| 引用本文： | 赵军,高岩 . 二阶线性系统族的共同二次Lyapunov函数 [J]. 重庆师范大学学报(自然科学版), 2012, 0(4): 52-56 |
| 作者姓名： | 赵军 高岩 |
| 作者单位： | 湖北医药学院数理教研室;上海理工大学管理学院 |
| 基金项目： | 国家自然科学基金(No.10671126);上海市研究生创新基金(No.JWCXSL0901) |
| 摘 要： | 研究了二阶线性系统族共同二次Lyapunov函数的存在性问题。系统模型为∑Ai:x(t)=Aix(t),其中Ai∈R2×2为Hurwitz常矩阵。借助Lyapunov稳定性理论和矩阵理论,对子系统矩阵包含有限个对角阵和有限个具有复数特征值矩阵的二阶系统族,分3种情况证明了其存在共同二次Lyapunov函数,将存在共同二次Lyapunov函数的充分条件转化为若干个代数不等式,并基于定理的证明过程给出了一个共同二次Lyapunov函数的求法。验证该充分条件容易在计算机上编程实现,从而具有较强的工程实用性。最后通过数值算例来验证了该充分条件的有效性以及更低的保守性。 |
| 关 键 词： | 共同二次Lyapunov函数 线性系统族 切换系统 |
Common Quadratic Lyapunov Functions for Second Order Linear Systems |
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| ZHAO Jun,GAO Yan . Common Quadratic Lyapunov Functions for Second Order Linear Systems [J]. Journal of Chongqing Normal University:Natural Science Edition, 2012, 0(4): 52-56 |
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| Authors: | ZHAO Jun GAO Yan |
| Affiliation: | 1(1.Dept.of Mathematics and Physics,Hubei University of Medicine,Shiyan Hubei 442000; 2.Business School,University of Shanghai for Science and Technology,Shanghai 200093,China) |
| Abstract: | The existence of the common quadratic Lyapunov functions of a set of second order linear systems is investigated.For a set of given second order linear systems ∑Ai:x(t)=Aix(t),where Ai∈R2×2 is Hurwitz matrix,it is proved that there exist common quadratic Lyapunov functions.The proposed sufficient conditions of the existence of common quadratic Lyapunov functions are obtained in form of algebra inequalities.And the method of seeking a common quadratic Lyapunov function is also given.It is convenient to verify the conditions by computer programming.Finally,numerical examples are given to show the effectiveness of the obtained results. |
| Keywords: | common quadratic Lyapunov functions linear systems switched linear systems |
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