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Existence conditions for L_1 Lyapunov functions for a class of nonautonomous systems

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2 Author(s)

A class of natural Lyapunov functions of the form \Sigma \lambda _{i} |x_{i}|, \lambda _{i} > 0 , is considered for the stability analysis of a general class of nonautonomous differential equations associated with many physical systems. It is shown that recent results on the existence of solutions to a class of linear inequalities directly yield necessary and sufficient conditions for the existence of a Lyapunov function of the form described.

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Circuit Theory, IEEE Transactions on  (Volume:19 ,  Issue: 6 )