Abstract

We consider a periodic selector-linear differential inclusion. It is proved that for this inclusion to be uniformly asymptotically stable, it is necessary and sufficient that there exists a time-periodic Lyapunov function of a quasi-quadratic form. We derive estimates for the Lyapunov function that guarantee its positive definiteness and the existence of an infinitesimal upper limit.

中文翻译：

---

周期选择器-线性微分包含的渐近稳定性判据

摘要

我们考虑周期选择器-线性微分包含。证明为使该包含一致地渐近稳定，有必要存在一个准二次形式的时间周期Lyapunov函数。我们推导了Lyapunov函数的估计，这些函数保证了它的正定性和无限小上限的存在。