Remarks on the stability of a class of TCP-like congestion control models

This note addresses the global asymptotic stability of a class of nonlinear dynamical systems including delays in their representations. These systems are encountered in the modelling of the congestion control mechanisms for the Internet [F. Kelly, 2001], [S. Deb, et al., 2002]. The analysis makes use of some appropriate Lyapunov-Krasovskii functionals. The derived conditions are simple, and easy to check.

[1]  Sean P. Meyn,et al.  Bounds on the throughput of congestion controllers in the presence of feedback delay , 2003, TNET.

[2]  R. Srikant,et al.  How good are deterministic fluid models of Internet congestion control? , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[3]  Silviu-Iulian Niculescu,et al.  Additional dynamics in transformed time-delay systems , 2000, IEEE Trans. Autom. Control..

[4]  Anuradha M. Annaswamy,et al.  An adaptive Smith-controller for time-delay systems with relative degree n*≤2 , 2003, Syst. Control. Lett..

[5]  Frank Kelly,et al.  Mathematical Modelling of the Internet , 2001 .

[6]  Sean P. Meyn,et al.  Boundedness of utility function based congestion controllers in the presence of delay , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[7]  R. Srikant,et al.  Global stability of congestion controllers for the internet , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..