Stability Analysis of Two Closed-Loop Systems for Suppressing Transient Gain Excursions in an Erbium-Doped Fibre Amplifier

Stability analysis of two closed-loop systems for suppressing transient gain excursions in an erbium-doped fibre amplifier (EDFA) is presented. A model applicable to both closed-loop systems is presented in the form of a nonlinear continuous switched system. The key objective of the stability analysis is to prove that the region of attraction of the asymptotically stable equilibrium point contains all the initial conditions encountered in practical realisations of the two closed-loop systems. This objective is accomplished by application of the Poincare-Bendixson theorem for planar systems. To apply the theorem, the existence of periodic state vector trajectories is ruled out by application of an extension of the traditional Bendixson theorem. Simulation results, which support the conclusions of the stability analysis, are also presented