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Local and global stability of symmetric heterogeneously-delayed control systems

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2 Author(s)
Yueping Zhang ; Texas A&M Univ., College Station, TX, USA ; Loguinov, D.

Stability proofs of nonlinear congestion control systems under heterogeneous feedback delays are usually difficult and involve a fair amount of effort. In this paper, we show that there exist a class of congestion control methods that admit very simple proofs of asymptotic stability and allow control equations to be delay-independent. This is in contrast to most previous work, which requires that each flow (and sometimes each router) adapt its control-loop constants based on the feedback delay and/or the length of the corresponding end-to-end path. Our new congestion control method, which we call Max-min Kelly Control (MKC), builds upon the work of Kelly et al. (1998) and allows end-flows to be stable and fair regardless of network feedback delays or the number of hops in their end-to-end paths. Using basic matrix algebra and discrete control theory, we show no's local asymptotic stability under heterogeneous, directional feedback delays. We also offer a simple proof of its global asymptotic stability assuming constant feedback delay.

Published in:

Decision and Control, 2004. CDC. 43rd IEEE Conference on  (Volume:5 )

Date of Conference:

14-17 Dec. 2004

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