Abstract
In this paper, we derive a necessary condition for local asymptotic stability of equilibria of nonlinear systems with parameters. As a corollary of our general result, we deduce Brockett's necessary condition for local asymptotic stability of equilibria of nonlinear autonomous systems. The proof we give, however, is quite different from the existing proofs in the literature. We show by way of an example that our new necessary condition is stronger than Brockett's necessary condition, but retains much of the user-friendly appeal of Brockett's criterion. We further illustrate our result with more examples. Copyright © 2001 John Wiley & Sons, Ltd.
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