Let dx/dt = f(t,x) be a smooth differential equation in R×R^n and M be an s--compact invariant set in Rx R^n. Assume the existence of a smooth invariant set Φ in R×Rn containing M such that M is uniformly asymptotically stable with respect to the perturbations lying on Φ. We analyze the influence of the stability properties of Φ "near M" on the unconditional stability properties of M. A comparison with some classical results concerning the autonomous or the periodic case is also given.

Conditional and unconditional stability properties of time dependent sets

VISENTIN, FRANCESCA
2005

Abstract

Let dx/dt = f(t,x) be a smooth differential equation in R×R^n and M be an s--compact invariant set in Rx R^n. Assume the existence of a smooth invariant set Φ in R×Rn containing M such that M is uniformly asymptotically stable with respect to the perturbations lying on Φ. We analyze the influence of the stability properties of Φ "near M" on the unconditional stability properties of M. A comparison with some classical results concerning the autonomous or the periodic case is also given.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11588/12363
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