Abstract
In this article, the problems of exponential stability analysis and stabilisation of linear time-varying systems described by a class of second-order vector differential equations are considered. Using bounding techniques on the trajectories of a linear time-varying system, the stability problem of the time-varying system is transformed to that of a time-invariant system and a new sufficient condition for the exponential stability is obtained. Moreover, the new criterion is proven to be superior to a test presented in the recent literature. Finally, the proposed criterion is applied to the exponential stabilisation problem via state feedback. The results are illustrated by several numerical examples.
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