NECESSARY AND SUFFICIENT CONDITIONS FOR STABILITY OF MRAC SYSTEMS
Antonio Loria, Elena Panteley
We present necessary and sufficient conditions for uniform global asymptotic stability of Model-Reference Adaptive Control (MRAC) systems. Our conditions are stated in terms of a notion of persistency of excitation (PE) that is tailored for {\em nonlinear} systems; in particular, it applies to functions of time and state and allow critical cases such as vanishing at the origin. Thus, this property generalizes classical PE and rigourously settles conditions that were previously inferred without strict proof.