Abstract
Difficulty is often encountered in stability analysis in the construction of Liapunov functions for systems. Also Liapunov' theorems often only ensure stability when asymptotic stability is required when [Vdot](X) is semi-definite. The theorem presented enables asymptotic stability information to be obtained when [Vdot](X) is semi-definite in regions of state space where other theorems only ensure stability.
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