  It is typically proven in adaptive control that asymptotic stabilization and
tracking holds, and that at best a bounded-noise bounded-state property is
proven. Recently, it has been shown in both the pole-placement control and the
$d$-step ahead control settings that if, as part of the adaptive controller, a
parameter estimator based on the original projection algorithm is used and the
parameter estimates are restricted to a convex set, then the closed-loop system
experiences linear-like behavior: exponential stability, a bounded gain on the
noise in every $p$-norm, and a convolution bound on the exogenous inputs; this
can be leveraged to provide tolerance to unmodelled dynamics and plant
parameter time-variation. In this paper, we extend the approach to the more
general Model Reference Adaptive Control (MRAC) problem and demonstrate that we
achieve the same desirable linear-like closed-loop properties.
