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.