Behaviour of the output error identification algorithm for small stepsize gains (Q1064308)

In the output error identification algorithm, it is possible to adjust a given parameter to trade off, for example, sensitivity to noise and capacity to track plant parameter variations. The rate of convergence of the ideal algorithm (obtained in the noise free, time-invariant plant parameter case) is related to the magnitude of this gain parameter. The analysis applies to a broader class of adaptive problems than output error identification, and in particular, a positive real transfer function appearing in the problem formulation is allowed to be nonrational. An alternative to the usual Lyapunov-based analysis is then needed.