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.
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