Abstract
Recently it has been shown how to carry out adaptive control for an 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. The goal of this paper is to show that this robustness property is true for a general adaptive controller which may include multi-estimators; the immediate ramification is that if we are able to prove exponential stability and a convolution bound for the case of fixed plant parameters, then robustness comes for free.