Summability characterizations of uniform exponential and asymptotic stability of sets for difference inclusions
AR Teel, D Nesic, A Loria, E Panteley
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | TAYLOR & FRANCIS LTD | Published : 2010
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. © 2010 Taylor & Francis.
This work was partially supported by the Australian Research Council under the Australian Professorial Fellow and Discovery Grant schemes.