Asymptotic stability equals exponential stability, and ISS equals finite energy gain - if you twist your eyes

Authors
Grune, L Sontag, ED Wirth, FR
Citation
L. Grune et al., Asymptotic stability equals exponential stability, and ISS equals finite energy gain - if you twist your eyes, SYST CONTR, 38(2), 1999, pp. 127-134
Citations number
37
Categorie Soggetti
AI Robotics and Automatic Control
Journal title
SYSTEMS & CONTROL LETTERS
ISSN journal
01676911 → ACNP
Volume
38
Issue
2
Year of publication
1999
Pages
127 - 134
Database
ISI
SICI code
0167-6911(19991004)38:2<127:ASEESA>2.0.ZU;2-J
Abstract
In this paper we show that uniformly global asymptotic stability for a fami ly of ordinary differential equations is equivalent to uniformly global exp onential stability under a suitable nonlinear change of variables. The same is shown for input-to-state stability and input-to-state exponential stabi lity, and for input-to-state exponential stability and a nonlinear H-infini ty estimate. (C) 1999 Elsevier Science B.V. All rights reserved.