Lyapunov-based Stability Analysis of a One-Pump One-Signal Co-pumping Raman Amplifier.

摘要

We consider the boundary control problem to stabilize the power of a signal and a pump propagating down a Raman amplifier. This is essentially an initial-boundary value problem (IBVP) of a hyperbolic system with Lotka-Volterra type nonlinearities. We treat the system as a control problem with states in the function space and use Lyapunov-based analysis to demonstrate asymptotic stability in the C0- and the L2-sense. The stability conditions are derived for closed-loop systems with a proportional controller and a dynamic controller, and confirmed by simulations in MATLAB.