Optical networks provide high data transmission rates which require optimal power control algorithms to ensure the proper delivery of the signals. Time-delays may destabilize the control algorithms. We study the stability of game-theoretic based primal-dual control algorithms applied to multi-link single-sink optical networks. We present a perturbed optical signal-to-noise ratio (OSNR) model with time-delays. By optimizing the OSNR values, we reduce the bit error rates of the channels. We modify singular perturbation theory to include Lyapunov-Krasovskii stability theory with multiple time-delays and uncertainties. Simulations show the stabilization of perturbed systems at the expense of transient convergence time. (C) 2013 Elsevier Ltd. All rights reserved.