A stability analysis with time-delay of primal–dual power control in optical links

Primal-dual power control algorithms in optical networks must be designed properly to remain stable in the presence of time-delays. Control algorithms at the signal transmitters continuously update their channel powers in response to dynamic pricing information from the network links. The control algorithms optimize the optical signal-to-noise ratios (OSNRs) of the channels in a distributive and non-cooperative manner. We consider the case of a single link with multiple channels and a constant time-delay. These results also apply to single sink general network configurations if the time-delay represents the longest round-trip time in the network. We derive sufficient conditions for the stability of the closed loop system based on a tunable parameter in the control algorithm. The work combines singular perturbation theory with Lyapunov–Razumikhin time-delay techniques. We verify our results through simulations based on realistic network parameters.