Asymptotic Properties of Nonlinear Singularly Perturbed Volterra Equations∗. Issue 11 (2015)

• Record Type: Journal Article
• Authors: Smirnova, Vera B.; Pak, Ella E.; Proskurnikov, Anton V.; Utina, Natalia V.
• Is Part Of: IFAC-PapersOnLine. Volume 48:Issue 11(2015)
• Page Start: 604
• Page End: 609
• Publication Date: 2015
• Subjects: Nonlinear systems -- absolute stability -- Volterra equations -- singular perturbation; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2015.09.253
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: In this paper we examine asymptotic behavior of dynamics systems in the Lur'e form, that can be decomposed into feedback interconnection of a linear part and a time-varying nonlinearity. The linear part obeys a singularly perturbed integro-differential Volterra equation of the convolutional type, whereas the nonlinearity is sector-bounded. For such a system we propose frequency-domain criteria of the stability and the "gradient-like" behavior, i.e. the attraction of any solution to one of equilibria points. Those criteria, based on the V.M. Popov's method of a priori integral indices, are uniform with respect to the small parameter.