Generalized practical stability analysis of discontinuous dynamical systems
Generalized practical stability analysis of discontinuous dynamical systems
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DOI：
10.1109/cdc.2003.1272851
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发表时间：
2003-12
期刊：
影响因子：
--
通讯作者：
G. Zhai;A. Michel
中科院分区：
文献类型：
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作者：
G. Zhai;A. Michel
在实践中，人们不仅对李雅普诺夫稳定性提供的定性特征感兴趣，而且对有关系统行为的定量信息感兴趣，包括可能在有限时间间隔内的轨迹边界的估计。这类信息过去曾使用实际稳定性概念系统地确定过。本文给出了广义实用稳定性（简称GP-稳定性）的一个新定义，并建立了一类不连续动力系统GP-稳定性的充分条件。在经典的李雅普诺夫理论，我们的结果构成了一个直接的方法，利用辅助标量值的李雅普诺夫函数。然而，这些函数的性质与通常的李雅普诺夫函数有很大的不同。我们证明了我们的结果的适用性，通过几个具体的例子。
In practice, one is not only interested in the qualitative characterizations provided by Lyapunov stability, but also in quantitative information concerning system behavior, including estimates of trajectory bounds, possibly over finite time intervals. This type of information has been ascertained in the past in a systematic manner, using the concept of practical stability. In the present paper, we give a new definition of generalized practical stability (abbreviated as GP-stability) and establish some sufficient conditions concerning GP-stability for a wide class of discontinuous dynamical systems. As in the classical Lyapunov theory, our results constitute a direct method, making use of auxiliary scalar-valued Lyapunov-like functions. These functions, however, have properties that differ significantly from the usual Lyapunov functions. We demonstrate the applicability of our results by means of several specific examples.