Parameter drift instability in adaptive systems

An error model describing a variety of adaptive systems is studied, representing applications in adaptive filtering, recursive parameter identification, and model reference adaptive control. For the a posteriori or normalized type of adaptive law in the output error form, it is shown that error model instability requires a specific type of drift instability. Such drift is nonexplosive, but can lead to unbounded parameter and prediction errors. Drift is known to occur in the presence of algorithm disturbances, but a recent conjecture suggests it cannot happen in the ideal, no-disturbance case. Concrete examples are given showing drift to occur in this ideal case, provided a strictly positive real condition is violated