Uncertainty Principles and Identification n-Widths for LTI and Slowly Varying Systems

In the identification of LTI systems, the optimal worst-case uncertainty depends on the observation time. This dependence is characterized via two notions of n-width, which are computed in the l¹ and H^¿ norms. The results are then applied to systems in which the law governing the evolution of the uncertain elements is not time invariant. Such systems can not be identified accurately. The inherent uncertainty is bounded in the case of slow time variation.