A Small Gain Approach to Delay Robustness of Networks.dvi

This paper studies the stability of a network flow model with transmission and queuing delays in the forward and backward channels. We present a novel small gain approach to prove global asymptotic stability for arbitrary time delays and network routing. This approach uses a logarithmic state transformation suggested recently in the literature, and establishes a linear input-to-state gain for the transformed system. With the new state variables the gain of the routing matrix is unity and, thus, the stability condition is scalable and independent of routing. Unlike existing results that employ the logarithmic transformation, we give a simple small-gain interpretation for ∗ Corresponding author. Electrical, Computer and Systems Engineering Department, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA. Tel.: +1-518-276-8205; fax: +1-518-276-6261.