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A Criterion for the Asymptotic Stability of a Periodic Selector-Linear Differential Inclusion
Automation and Remote Control ( IF 0.6 ) Pub Date : 2021-02-25 , DOI: 10.1134/s0005117921010045 M. V. Morozov
中文翻译:
周期选择器-线性微分包含的渐近稳定性判据
更新日期:2021-02-25
Automation and Remote Control ( IF 0.6 ) Pub Date : 2021-02-25 , DOI: 10.1134/s0005117921010045 M. V. Morozov
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。