Existence conditions forL_1Lyapunov functions for a class of nonautonomous systems

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.