Asymptotic Properties of Nonlinear Singularly Perturbed Volterra Equations

摘要

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.