Persistence of equilibria for locally asymptotically stable systems

Citation
Ci. Byrnes et V. Sundarapandian, Persistence of equilibria for locally asymptotically stable systems, INT J ROBUS, 11(1), 2001, pp. 87-93
Citations number
8
Categorie Soggetti
AI Robotics and Automatic Control
Journal title
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
ISSN journal
10498923 → ACNP
Volume
11
Issue
1
Year of publication
2001
Pages
87 - 93
Database
ISI
SICI code
1049-8923(200101)11:1<87:POEFLA>2.0.ZU;2-#
Abstract
In this paper, we derive a necessary condition for local asymptotic stabili ty of equilibria of nonlinear systems with parameters. As a corollary of ou r general result, we deduce Brockett's necessary condition for local asympt otic stability of equilibria of nonlinear autonomous systems. The proof we give, however, is quite different from the existing proofs in the literatur e. We show by way of an example that our new necessary condition is stronge r than Brockett's necessary condition, but retains much of the user-friendl y appeal of Brockett's criterion. We further illustrate our result with mor e examples. Copyright (C) 2001 John Wiley & Sons, Ltd.