On Bifurcation Control in Time Delay Feedback Systems

Abstract

The paper addresses bifurcations of limit cycles for a class of feedback control systems depending on parameters. A set of simple approximate analytical conditions characterizing all the generic limit cycle bifurcations is determined via a first-order harmonic balance analysis in a suitable frequency band. Based on the results of this analysis, an approach to limit cycle bifurcation control is proposed. In particular, an example concerning a biological delay model is developed, where a flip bifurcation control is designed via a modified Pyragas technique.