ABSTRACT

In this paper, we establish a new criterion for robustness of global asymptotic stability of zero solution of LTV system $\dot{x}=A(t)x$ in the presence of external perturbations (disturbances). To prove the result, logarithmic norm will be used under which the stability becomes a topological notion depending on the chosen vector norm in the state-space ${\mathbb{R}}^n.$

中文翻译：

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全局渐近稳定性对线性时变系统外部摄动鲁棒性的判据

摘要

本文为LTV系统零解的全局渐近稳定性的鲁棒性建立了新的判据。 $\dot{X}=\mathrm{一种}（Ť）X$在外部干扰（干扰）的情况下。为了证明结果，将使用对数范数，根据状态空间中选择的矢量范数，稳定性将成为拓扑概念${\mathbb{[R}}^{ñ}。$