Dynamic time-delayed feedback control of Westwood plus TCP flow control model with communication delay

In this article, we consider the problem of Hopf bifurcation control in a second-order Westwood+ TCP flow control model. First, we propose a dynamic time-delayed state feedback controller to delay the onset of undesirable Hopf bifurcation. Moreover, we show that the Westwood+ TCP model with time-delayed state feedback can maintain a stationary state on a certain domain in the delay parameter space. In particular, by the dynamic time-delayed feedback controller, a suitable Hopf bifurcation is created at a desired location with preferred properties. Furthermore, we analyse the dynamic behaviour of the rightmost characteristic root of the proposed controlled time-delayed systems via Lambert W function. In addition, by the Hopf bifurcation analysis, we show that with the proposed controller, one can increase the allowable critical value of the communication delay, and postpone the onset of the undesired Hopf bifurcation by successfully controlling unstable steady states or periodic orbits. Finally, we justify by numerical results the validity of the time-delayed state feedback controller in Hopf bifurcation control.