Lyapunov-like solutions to stability problems for discrete-time systems on asymptotically contractive sets (Q1303138)

Criteria for stability properties of discrete-time nonstationary systems are presented based upon the concept of asymptotic contractive sets. It is shown that the classical Lyapunov stability conditions including the invariance principle by LaSalle cannot be applied to the stability test once the system instantaneous domain of asymptotic stability is asymptotically contractive. The results determine good estimates of domains of asymptotic stability having several kinds of stability properties.