Stability robustness of adaptive systems requires only lower bounds on excitation

New results for basic algorithm robustness are given. Recent descriptions of a self-stabilization mechanism present in a posteriori adaptive algorithm indicate that parameter drift instability is necessary for bounded disturbances to lead to unbounded parameter and prediction errors. It is also known that some forms of persistent excitation conditions can prevent parameter drift. The author provides a proof that only lower bounds on persistent excitation are sufficient for bounded-disturbance bounded-error stability. This result significantly extends stability theory for adaptive systems, since it does not restrict disturbances to be small relative to the level of excitation, as in the standard perturbation-style analyses