Stability Analysis of XCP Congestion Control Systems

This paper studies the stability of explicit control protocol (XCP). The control-theoretic framework used in most of the previous work is linear system theory. Based on the linearization of nonlinear congestion control systems, classical linear techniques, such as the Nyquist or Bode criteria, are applied for the analysis of stability. The success of the linearization method depends on the assumption that the equilibrium is far away from the zero queue length point so that the linearization is well- defined. In this paper, taking account of the physical constraint of the queue length, i.e., queue lengths never being negative, the dynamics of XCP is modeled as one class of linear switched time-delay systems. For such systems, classic linear approaches do not work any more. Instead, we employ Lyapunov approach by constructing one piecewise continuous quadratic Lyapunov functional. Under such Lyapunov functional, stability results are established for determining the parameters of XCP systems. This Lyapunov method actually also provides us a technique of handling linear switched time-delay systems.