On Delay-Independent Diagonal Stability of Max-Min Congestion Control

Yueping Zhang, Dmitri Loguinov
2006 Proceedings of the 45th IEEE Conference on Decision and Control  
Network feedback in a congestion-control system is subject to delay, which can significantly affect stability and performance of the entire system. While most existing stability conditions explicitly depend on delay Di of individual flow i, a recent study [24] shows that the combination of a symmetric Jacobian A and condition ρ(A) < 1 guarantees local stability of the system regardless of Di. However, the requirement of symmetry is very conservative and no further results have been obtained
more » ... e been obtained beyond this point. In this paper, we proceed in this direction and gain a better understanding of conditions under which congestion-control systems can achieve delayindependent stability. Towards this end, we first prove that if Jacobian matrix A satisfies ||A|| < 1 for any monotonic induced matrix norm ||.||, the system is locally stable under arbitrary diagonal delay Di. We then derive a more generic result and prove that delay-independent stability is guaranteed as long as A is Schur diagonally stable [9], which is also observed to be a necessary condition in simulations. Utilizing these results, we identify several classes of well-known matrices that are stable under diagonal delays if ρ(A) < 1 and prove stability of MKC [24] with arbitrary parameters αi and βi.
doi:10.1109/cdc.2006.377630 dblp:conf/cdc/ZhangL06 fatcat:bco3fbkygbaxjppbwo4mhwur64