F. Watbled
Titre:
"On singular perturbations for differential inclusions on the infinite interval."
Abstract:
We consider a differential inclusion subject to a singular perturbation,
i.e. part of the derivatives are multiplied by a small
parameter $\epsilon >0$.
We show that under some stability and
structural assumptions, every solution
of the singularly perturbed inclusion comes close
to a solution of the degenerate inclusion (obtained for $\epsilon=0$)
when $\epsilon$ tends to 0.
The goal of the present paper is to provide a new result of
Tikhonov type on the time interval $[0,+\infty[$.
Key words:
Singular perturbation,
differential inclusions, asymptotic stability,
Liapunov functions, Tikhonov's theorem.