Smooth Lyapunov functions and robustness of stability for difference inclusions

摘要

We demonstrate the equivalence of robust global asymptotic stability (GAS) of the origin and the existence of a smooth Lyapunov function for difference inclusions defined by upper semicontinuous set-valued maps. Sufficient conditions for robust GAS are given. As an application of these results, we give conditions for robust GAS of difference equations defined by discontinuous right-hand sides. (C) 2004 Elsevier B.V. All rights reserved.