Accuracy Confidence Bands Including The Bias Of Model Under-Fitting

New results are developed that give accuracy confidence bands based upon the parameter estimation error of system identification including the bias of model under-fitting. In this context, bias means the underestimation of model accuracy due to selection of the model state order than the true system order. It is shown that the optimal accuracy model is given by the model minimizing the Akaike information criterion (AIC), and that the bias is indicated by the behavior of the AIC as a function of model order beyond the minimum order. The resulting confidence bands are simultaneous so that they guarantee the system frequency response function lies entirely within the band for all frequencies with the stated probability. Such bands are then appropriate for guaranteeing robust stability and performance of robust controllers.