  Recently, a new approach to the adaptive control of linear time-invariant
plants with unknown parameters (referred to as second level adaptation), was
introduced by Han and Narendra in [1]. Based on $N (\geq m+1)$ fixed or
adaptive models of the plant, where $m$ is the dimension of the unknown
parameter vector, an unknown parameter vector $\alpha\in R^{N}$ is estimated in
the new approach, and in turn, is used to control the overall system.
Simulation studies were presented in [1] to demonstrate that the new method is
significantly better than those that are currently in use.
  In this paper, we undertake a more detailed examination of the theoretical
and practical advantages claimed for the new method. In particular, the need
for many models, the proof of stability, and the improvement in performance and
robustness are explored in depth both theoretically and experimentally.
