Lyapunov stability criteria are derived for a first-order closed-loop adaptive-optics servo system, resulting in a linear matrix equation that includes the system geometry, servo parameters, and wave-front reconstruction 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 Lyapunov equation. The significance of these results is discussed.
© 1998 Optical Society of America
Walter J. Wild, "Lyapunov stability criteria for zonal adaptive-optics systems," Opt. Lett. 23, 570-572 (1998)