On Delay-Independent Diagonal Stability of Max-Min Congestion Control
Yueping Zhang, Dmitri Loguinov · IEEE Transactions on Automatic Control · 2009
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 Diof individual flowi, a recent study shows that the combination of a symmetric JacobianAand condition p(A)i. However, the requirement of symmetry is very conservative and no further results have been obtained beyond this point. In this technical note, we proceed in this direction and gain a better understanding of conditions under which congestion-control systems can achieve delay-independent stability. Towards this end, we first prove that if Jacobian matrixAsatisfies ||A||i. We then derive a more generic result and prove that delay-independent stability is guaranteed as long asAis Schur diagonally stable , 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 rho(A)iand betai.