— Adaptive control architectures often make use of
Lyapunov functions to design adaptive laws. We are specifically
interested in adaptive control methods, such as the well-known
L1 adaptive architecture, which employ a parameter observer
for this purpose. In such architectures, the observation error
plays a critical role in determining analytical bounds on the
tracking error as well as robustness. In this paper, we show how
the non-existence of coercive Lyapunov operators can impact
the analytical bounds, and with it the performance and the
robustness of such adaptive systems.