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 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.
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