论文标题
奇异扰动线性开关系统的最大Lyapunov指数的上限和下限
Upper and lower bounds for the maximal Lyapunov exponent of singularly perturbed linear switching systems
论文作者
论文摘要
在本文中，我们考虑了确定唯一干扰线性开关系统的稳定性属性，尤其是评估指数稳定性的问题。这个问题的挑战之一是源于单数扰动的小参数和开关速率之间的复杂相互作用，因为两者都趋于零。我们的方法包括表征合适的辅助线性系统，该系统为线性开关系统的最大Lyapunov指数的渐近学提供了下层和上限，因为奇异扰动的参数趋向于零。
In this paper we consider the problem of determining the stability properties, and in particular assessing the exponential stability, of a singularly perturbed linear switching system. One of the challenges of this problem arises from the intricate interplay between the small parameter of singular perturbation and the rate of switching, as both tend to zero. Our approach consists in characterizing suitable auxiliary linear systems that provide lower and upper bounds for the asymptotics of the maximal Lyapunov exponent of the linear switching system as the parameter of the singular perturbation tends to zero.
