A STABILITY-INSTABILITY BOUNDARY FOR DISTURBANCE-FREE SLOW ADAPTATION WITH UNMODELED DYNAMICS

The instability of adaptive schemes for small values of parameter adjustment gain has the form of a slow drift of adjustable parameters. Using an averaging analysis, the authors derive not only a sufficient condition for stability of this drift, but also a sufficient condition for it to be unstable. A sharp boundary between stability and instability is signal dependent and much less demanding than the usual strict positive realness property. The new positivity condition has a simple signal energy interpretation.