On the local stability properties of adaptive parameter estimators with composite errors and split algorithms

The stability characteristics of a generalized error system structure are examined for adaptive parameter estimation systems. This error system form encompasses the structure of a number of particular applications of adaptive parameter estimation theory which fall outside the framework of more familiar error system models. The consequences for error system stability which derive from the added generality are analyzed. It is demonstrated that, when using averaging theory techniques to analyze the error system, stability conditions must be augmented for the basic error system in order to ensure stability for the generalized error system. The inadequacy of regressor spectral restrictions and persistent spanning conditions to guarantee local error system stability of the generalized structure is rigorously established. Alternative conditions which will yield such local stability are demonstrated. To illustrate the concepts involved, the recursive identification of parameters is examined in a parallel-form realization of a linear system