Journal of Applied Mathematics
Volume 2007 (2007), Article ID 72561, 12 pages
Research Article

Oscillatority Conditions for Nonlinear Systems with Delay

Denis V. Efimov1 and Alexander L. Fradkov2

1Laboratoire des Signaux et Systémes (L2S), Supélec, Gif-sur-Yvette 91192, France
2Control of Complex Systems (CCS) Laboratory, Institute for Problems of Mechanical Engineering (IPME), Bolshoi Avenue 61, V.O., St. Petersburg 199178, Russia

Received 16 February 2006; Revised 22 November 2006; Accepted 7 February 2007

Academic Editor: Henk Nijmeijer

Copyright © 2007 Denis V. Efimov and Alexander L. Fradkov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Sufficient conditions for oscillatority in the sense of Yakubovich for a class of time delay nonlinear systems are proposed. Under proposed conditions, upper and lower bounds for oscillation amplitude are given. Examples illustrating analytical results by computer simulation are presented.