Stability Analysis of Proportional–Integral AQM Controllers Supporting TCP Flows

Análisis de Estabilidad de Controladores AQM Proporcional–Integral Suportando Flujos TCP

Daniel Melchor Aguilar* and Víctor Castillo Torres

División de Matemáticas Aplicadas, IPICyT, A.P. 3–74, 78216, San Luis Potosí, SLP, México dmelchor@ipicyt.edu-mx *

Article received on February 28, 2007
Accepted on September 04, 2007

Abstract

This paper focuses on the asymptotic stability of proportional–integral AQM controllers supporting TCP flows. Necessary and sufficient conditions for the asymptotic stability of the closed–loop linearization are provided. As a result, the complete set of proportional–integral controllers that locally stabilizes the equilibrium point is obtained. The robustness of the controllers to uncertainties in the network parameters (number of TCP flows, round–trip time and link capacity) is also addressed. It is shown that designing the controller with respect to the largest expected values of delay and link capacity, and the smallest expected value of TCP loads leads to the complete set of robust stabilizing controllers.

Keywords: Proportional–Integral AQM controllers, Stability, Robust Stability, Time–Delay Systems.

Resumen

Este artículo se centra en la estabilidad asintótica de controladores AQM del tipo proporcional–integral suportando flujos TCP . Se proporcionan condiciones necesarias y suficientes para la estabilidad asintótica de la linealización del sistema en lazo cerrado. Como un resultado, se obtiene el conjunto completo de controladores proporcional–integral que estabiliza localmente el punto de equilibrio. También se aborda la robustez de los controladores a incertidumbres en los parámetros de red (número de sesiones TCP, tiempo de viaje completo y capacidad del enlace). Se muestra que diseñando el controlador con respecto a los valores más grandes esperados para el retardo y la capacidad del enlace, y el valor más pequeño esperado para las cargas de TCP nos proporciona el conjunto completo de controladores robustos.

Palabras clave: Controladores AQM proporcional–integral; Estabilidad; Estabilidad Robusta; Sistemas con retardos.

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Acknowledgments

The authors would like to thank the anonymous reviewers of the paper for their constructive suggestions that helped us to improve the paper. This work was partially funded by the CONACyT grant: Análisis de Estabilidad y Estabilidad Robusta de Controladores de Flujo en Internet (2007–2008).

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