On the use of the method of averaging for the stability analysis of adaptive linear control systems

The uses and limitations of the method of averaging are discussed with application of linear parameter adaptive systems. The method of averaging has shown to provide a means to explicitly determine some of the important aspects of adaptive system performance, but there are inherent limitations, e.g., slow adaptation and parameters restricted to trajectories within the constant parameter stability set. Remedies to alleviate these restrictions are discussed, based primarily on the use of a fixed point analysis.