Parameter drift instability in disturbance-free adaptive systems

Adaptive identification and control algorithms can exhibit local instability when certain ideal assumptions, such as satisfaction of strictly positive real (SPR) conditions, are violated. However, conjectures suggest that due to a self-stabilization mechanism, global boundedness may still hold despite local instabilities. Counterexamples to these are presented, showing that self-stabilization is bypassed via hidden unbounded parameter drift. Although parameter drift instability is known to occur in adaptive systems with disturbances, concrete examples are given to show that unbounded drift can also occur in the disturbance-free case when SPR conditions are violated