A. M. Krasnosel'skii, D. I. Rachinskii, “Criteria of resonance origin in a single-circuit control system with saturation”, Avtomat. i Telemekh., 2008, Issue 8,Pages <nobr>33

Deterministic Systems

Criteria of resonance origin in a single-circuit control system with saturation

A. M. Krasnosel'skii^a, D. I. Rachinskii^ab

^a Institute for Information Transmission Problems Russian Academy of Sciences, Moscow, Russia
^b University College Cork, Cork, Ireland

Abstract: Studies are made of forced periodic oscillations in a single-circuit control system with a parameter, the dynamics of which is described by resonance equations in the linear approximation. Criteria are suggested of the origin of resonance that is understood as an increase to infinity of the amplitude of forced oscillations in the approximation of the parameter to certain critical values. The principal results relate to the case when answers are defined by bounded nonlinearities of the order of a constant; the summands that decrease to zero are of no importance.

PACS: 02.30.Hq

Presented by the member of Editorial Board: B. T. Polyak

Received: 03.04.2007