Computing non-fragile PI controllers for delay models of TCP/AQM networks

Abstract

This article focuses on the stabilisation problem of fluid-flow delay models of transmission control protocol/active queue management (TCP/AQM) networks by using a proportional-integral (PI) controller as AQM strategy. More precisely, the complete set of PI controllers that exponentially stabilises the corresponding linear time-delay system is derived. Using the particular geometric properties of this set of the controller parameters, the issues of robustness to uncertainty in the network parameters and to perturbation in the controller coefficients are addressed. Then, a methodology to compute a non-fragile PI AQM controller is provided. Finally, exponential estimates for the closed-loop system solutions, allowing to evaluate the performance of the corresponding PI-controlled closed-loop system, are proposed by using a Lyapunov–Krasovskii functional approach. An illustrative example completes the presentation.

Keywords:

• PI AQM controllers
• robustness
• fragility
• time-delay systems

Acknowledgements

This work was partially funded by the CNRS-CONACyT Grant: ‘Congestion Control Problem in Networks: A Delay System Approach’ (2007–2008). The authors wish to thank Professor Hitay Özbay from Bilkent University (Turkey) for his valuable comments on a preliminary version of this article as well as for pointing out some of the references cited in this work. The authors also wish to thank the anonymous reviewers of this article for their useful comments and suggestions that helped us to improve the work.