Abstract
This paper discusses the asymptotic stability of nonautonomous systems by means of the direct method of Liapunov. We assume existence of a positive time-invariant Liapunov function with negative semi-definite derivative. We focus on the extra conditions needed in order to guarantee asymptotic stability and present a theorem which offers a new criterion for asymptotic stability. The theorem is illustrated first by recovering Barbashin's principle for autonomous and periodic systems and second by studying the nonlinear pendulum with time-varying damping for which we derive a new asymptotic stability result.
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