LYAPUNOV STABILITY-CRITERIA FOR ZONAL ADAPTIVE-OPTICS SYSTEMS

Lyapunov stability criteria are derived for a first-order closed-loop adaptive-optics servo system, resulting in a linear matrix equation th at includes the system geometry, servo parameters, and wave-front reco nstruction matrix. It is demonstrated that instability zones depend on the choice of matrix estimator and the servo-loop gain. Divergence of the error propagator gives results that are consistent with the Lyapu nov equation. The significance of these results is discussed. (C) 1998 Optical Society of America.