Conditional and unconditional stability properties of time dependent sets

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.

Country

Italy

Related Organizations

University Federico II of Naples
Italy
University of Trento
Italy

Keywords

stability properties of sets, first integrals, invariance, invariance; first integrals; stability properties of sets

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