Criterion for robustness of global asymptotic stability to perturbations of linear time-varying systems

Abstract

In this brief note, we establish a novel criterion for robustness of global asymptotic stability of zero solution of LTV system $\dot x=A(t)x$ in the presence of possibly unbounded perturbations (external 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 $\mathbb{R}^n.$