A Note on Multiple Lyapunov Functions and Stability Condition for Switched and Hybrid Systems
A Note on Multiple Lyapunov Functions and Stability Condition for Switched and Hybrid Systems
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DOI：
10.1109/cca.2007.4389235
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发表时间：
2007-11
期刊：
影响因子：
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通讯作者：
G. Zhai;I. Matsune;J. Imae;Tomoaki Kobayashi
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文献类型：
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作者：
G. Zhai;I. Matsune;J. Imae;Tomoaki Kobayashi
在本文中，我们考虑切换和混合系统的多个李亚普诺夫函数的稳定性条件。利用评估每个子系统激活期间“多个Lyapunov函数的平均值”的思想，我们提出了一种新的Lyapunov稳定性条件，它补充了现有的评估多个Lyapunov函数在起点或终点的稳定性条件。我们提出了几个示范性例子，包括涉及不稳定子系统的情况，并将稳定性条件和切换策略应用于非完整系统稳定性的切换控制问题。
In this note, we consider stability condition with multiple Lyapunov functions for switched and hybrid systems. By using the idea of evaluating "the average value of multiple Lyapunov functions" during the activation period of each subsystem, we propose a new Lyapunov stability condition, which complements the existing stability conditions that evaluate the value of multiple Lyapunov functions at the starting points or the end points. We present several demonstrative examples, including the case where unstable subsystems are involved, and also apply the stability condition and the switching strategy to the switching control problem for stabilization of nonholonomic systems.