Asymptotic stability for damped strongly non-autonomous systems with applications to holonomic mechanical systems and nonlinear networks

Abstract

This paper deals with asymptotic stability for the solutions of ordinary differential systems with time dependent restoring potential of the type¶¶\( \nabla_p G(u,u^\prime))^\prime \,\,\, \nabla_u G(u,u^\prime) + q^m (t) f (u) = Q (t,u,u^\prime), \)¶¶ where Q may depends in an essential way on the variable u and can be not tame, a geometrical condition required in previous works. This allows us to extend a stability result concerning nonlinear networks to the non-autonomous case.