Hopf bifurcation control for a class of delay differential systems with discrete-time delayed feedback controller

This paper is concerned with the asymptotical stabilization for a class of unstable delay differential equations. Continuous-time delayed feedback controller (C-TDFC) and discrete-time delayed feedback controller (D-TDFC) are presented and studied, respectively. To our best knowledge, applying Hopf bifurcation theory to delay differential equations with D-TDFC is original and meaningful. The difficulty brought by the introduction of sampling period has been overcome. An effective control range which ensures the asymptotical stability of equilibrium for the system with C-TDFC is obtained. Sequently, another effective control range for the system with D-TDFC is gotten, which approximates the one of C-TDFCS provided that the sampling period is sufficiently small. Meanwhile, efforts are paid to estimate a bound on sampling period. Finally, the theoretical results are applied to a physiological system to illustrate the effectiveness of the two control ranges. Published by AIP Publishing.