Robust power control of optical links with time-delay

We derive robust stability conditions for game-theoretic based power control in optical links with time-delay. We consider a perturbed optical signal to noise ratio (OSNR) model in the presence of time-delays. Primal-dual control algorithms adjust the signal powers at the channel sources and receiver to optimize the OSNR values. The link utilization price is regularly updated and fed back to the source algorithms. We apply norm-bounded uncertainty techniques to derive algebraic stability criteria. The main theorem exploits time-decoupling in the primal-dual algorithms by utilizing singular perturbation theory modified to handle Lyapunov-Krasovskii time-delay techniques. We produce a new robust time-delay bound which generalizes the previous nominal time-delay result.