Hopf bifurcation control for a fluid flow model of internet congestion control systems via state feedback

This paper discusses a problem of Hopf bifurcation control for a fluid flow model of Internet congestion control systems by using a state feedback controller. The communication delay is chosen as the bifurcation parameter and it is shown that the Hopf bifurcation occurs and the uncontrolled system loses the stability when the bifurcation parameter passes through a critical value. However, under the state feedback control, the onset of the Hopf bifurcation is successfully delayed so that the stability domain can be extended. Moreover, the property of the bifurcating periodic solutions can be determined by adjusting the parameters of the linear part and non-linear part of the controller. Furthermore, we further investigate the effect of parameters of the system on the onset of the Hopf bifurcation as well. Both the theoretical analysis and the numerical simulation testify the validity of the state feedback controller in controlling Hopf bifurcations.