On singular perturbations for differential inclusions on the infinite interval

• Published in: Journal of mathematical analysis and applications Vol. 310; no. 2; pp. 362 - 378
• Main Author: Watbled, F.
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 15.10.2005; Elsevier
• Subjects: Asymptotic stability; Differential inclusions; Exact sciences and technology; Global analysis, analysis on manifolds; Lyapunov functions; Mathematical analysis; Mathematics; Optimization and Control; Ordinary differential equations; Sciences and techniques of general use; Singular perturbation; Tikhonov's theorem; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Asymptotic stability; Differential inclusions; Lyapunov functions; Singular perturbation; Tikhonov's theorem; Mathematical analysis; Differential inclusion; Tikhonov regularization; Lyapunov function
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2005.01.067

We consider a differential inclusion subject to a singular perturbation, i.e., part of the derivatives are multiplied by a small parameter ɛ > 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 ɛ = 0 ) when ɛ tends to 0. The goal of the present paper is to provide a new result of Tikhonov type on the time interval [ 0 , + ∞ [ .