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Summary: A trajectory based approach for stability robustness of nonlinear
systems with inputs
D. Angeli
Dip. Sistemi e Informatica, University of Firenze,
Via di Santa Marta 3, 50139 Firenze, Italy
angeli@dsi.unifi.it
Tel. +39 055 4796359 - Fax. +39 055 4796363
D. Nesic
Department of Electrical and Electronic Engineering,
The University of Melbourne
Parkville, 3010, Victoria, Australia
d.nesic@ee.mu.oz.au
Abstract
We show, for two di erent de nitions of semiglobal practical external stability, that the stability
property holds on semi-in nite time intervals if and only if it holds on arbitrarily long but nite time
intervals. These results have immediate applications in analysis of stability properties of highly oscillatory
systems with inputs using averaging or for systems with inputs that are slowly varying. Results are stated
for general
ows and the stability is given with respect to arbitrary (not necessarily compact) sets.
Keywords: Input-to-State Stability, Slowly varying systems, Averaging methods, Singular perturbations,
Robustness
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