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On stability analysis of linear discrete-time switched systems using quadratic Lyapunov functions

机译：基于二次Lyapunov函数的线性离散时间交换系统的稳定性分析

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The paper deals with the stability properties of linear discrete-time switched systems with polytopic sets of dynamics. The most classical and viable way of studying the uniform asymptotic stability of such a system is to check for the existence of a quadratic Lyapunov function. It is known from the literature that letting the Lyapunov function depend on the time-varying dynamic improves the chance that a quadratic Lyapunov function exists. We prove that the dependence on the dynamic can be actually assumed to be linear, with no prejudice on the effectiveness of the method. Moreover, we show that no gain in the sensibility is obtained if we allow the Lyapunov function to depend on the time as well. We conclude by showing that Lyapunov quadratic stability is a strictly stronger notion that uniform asymptotic stability.
机译：本文涉及具有多种式动态的线性离散时间交换系统的稳定性特性。研究这种系统的均匀渐近稳定性的最古典和可行的方法是检查二次Lyapunov功能的存在。从文献中众所周知，让Lyapunov函数取决于时变动态，提高了二次Lyapunov功能的可能性。我们证明可以实际假设对动态的依赖性是线性的，没有偏见的方法的有效性。此外，我们表明，如果我们允许Lyapunov函数依赖于时间，因此可以获得敏感性的收益。我们通过表明Lyapunov二次稳定性是一种严格较强的渐近稳定性的概念。

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