Summability Characterizations of Uniform Exponential and Asymptotic Stability of Sets For Difference Inclusions

Andrew Teel (1) , Dragan Nesic (2) , Antonio Loria (3) , Elena Panteley (3)

1 CCDC - Center for Control, Dynamical-Systems, and Computation [Santa Barbara]
2 Department of Electrical and Electronic Engineering [Melbourne]
3 L2S - Laboratoire des signaux et systèmes

We present several equivalent characterizations of uniform global exponential stability (UGES) and uniform global asymptotic stability (UGAS) of arbitrary closed (not necessarily compact) sets for non-linear difference inclusions. In particular, we provide several characterizations of these stability properties via summability criteria that do not require the knowledge of a Lyapunov function. We apply our results to prove novel-nested Matrosov theorems for UGES and UGAS of the origin for time-varying non-linear difference inclusions

Mots clés: stability; difference inclusions; sampled-data systems

Domaines: Systèmes dynamiques [math.DS]

Andrew Teel, Dragan Nesic, Antonio Loria, Elena Panteley. Summability Characterizations of Uniform Exponential and Asymptotic Stability of Sets For Difference Inclusions. Journal of Difference Equations and Applications, 2010, 16 (2-3), pp.173-194. ⟨10.1080/10236190902817844⟩. ⟨hal-00687416⟩