Abstract
This paper discusses asymptotic stability for nonautonomous systems by means of the direct method of Liapunov. We consider 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 propose a new criterion. The theorem is illustrated with a simple example: we discuss the harmonic oscillator with time-variant damping for which we derive a new asymptotic stability result.
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