| SOME PROBLEMS OF LYAPUNOV METHOD IN LINEAR CONTINUOUS-TIME SYSTEM |
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| 引用本文： | 黄琳,许钟灵. SOME PROBLEMS OF LYAPUNOV METHOD IN LINEAR CONTINUOUS-TIME SYSTEM[J]. 系统科学与复杂性, 1991, 0(3) |
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| 作者姓名： | 黄琳 许钟灵 |
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| 作者单位： | Department of Mechanics Peking University，Beijing 100871，China，Department of Electrical and Computer Engineering，University of Massachusetts，Amherst，M A.01003.U.S.A |
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| 摘 要： | In this paper,some problems of Lyapunov method in linear continuous-time systemare discussed.In part 1,some motivations are given.In part 2,in order to get a good estimate ofthe decaying time in the system,the concept of appropriate Lyapunov function is introduced andthe condition of the system is given to guarantee the existence of the appropriate Lyapunov functionAn application of the appropriate Lyapunov function is introduced to give the bound of time varyingperturbation for the stable system.In part 3,some extensions of the Lyapunov asymptotical stabilitytheorem are given,where the condition of the total derivative of the Lyapunov function along thetrajectory of the system can be reduced from negative definiteness to semi-negative definiteness andcommon quadratic forms with some reasonable conditions,the example shows the extensions areinteresting.
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SOME PROBLEMS OF LYAPUNOV METHOD IN LINEAR CONTINUOUS-TIME SYSTEM |
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| Huang Lin. SOME PROBLEMS OF LYAPUNOV METHOD IN LINEAR CONTINUOUS-TIME SYSTEM[J]. Journal of Systems Science and Complexity, 1991, 0(3) |
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| Authors: | Huang Lin |
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| Abstract: | In this paper,some problems of Lyapunov method in linear continuous-time systemare discussed.In part 1,some motivations are given.In part 2,in order to get a good estimate ofthe decaying time in the system,the concept of appropriate Lyapunov function is introduced andthe condition of the system is given to guarantee the existence of the appropriate Lyapunov functionAn application of the appropriate Lyapunov function is introduced to give the bound of time varyingperturbation for the stable system.In part 3,some extensions of the Lyapunov asymptotical stabilitytheorem are given,where the condition of the total derivative of the Lyapunov function along thetrajectory of the system can be reduced from negative definiteness to semi-negative definiteness andcommon quadratic forms with some reasonable conditions,the example shows the extensions areinteresting. |
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| Keywords: | Appropriate Lyapunov function Uniformly complete observability Uniformly asymptotical stability |
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