Model Reference Adaptive Control with Linear-like Closed-loop Behavior

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.