Inherent robustness in the adaptive control of a large class of systems

Recently it has been shown how to carry out adaptive control for a linear time-invariant (LTI) plant so that the effect of the initial condition decays exponentially to zero and so that the input-output behavior enjoys a convolution bound. This, in turn, has been leveraged to prove, in several special cases, that the closed-loop system is robust in the sense that both of these properties are maintained in the presence of a small amount of parameter time-variation and unmodelled dynamics. This paper shows that this robustness property is true for a general adaptive controller with the right properties: if we are able to prove exponential stability and a convolution bound for the case of fixed plant parameters, then robustness comes for free. We also apply the results to solutions to various adaptive control problems in the literature.