A frequency content condition for split algorithm-composite error adaptive system stability

Local stability for adaptive parameter estimation systems involving split algorithms and composite errors is considered from a frequency content viewpoint. Previous work has shown that definitive local stability conditions for these systems, phrased independently of regressor structure, are more restrictive than corresponding conditions for less general adaptive system models. In this paper, it is shown that by incorporating the regressor structure into the stability considerations, a frequency range for `good´ excitation can be described in the following sense. If the frequency content of the system excitation lies wholly within this `good´ range, then with satisfaction of certain persistent spanning conditions, the parameter estimator system will be locally stable. The task of analytically specifying the limits of this good frequency range is quite difficult; however it is possible to describe some qualitative properties of the frequency range which are helpful in the stable design of a split algorithm-composite error adaptive system