H2 and H∞ robust nonrational filtering for linear delay systems

This paper addresses the problem of robust filtering for uncertain linear signal models affected by time delays in the state. Uncertainty is structured and the model is assumed to lie in a given bounded polyhedral set. The main innovation is the use of a nonrational filter, that is, a filter that also contains delays in the filter state. Robust filtering performance is evaluated using the H₂ or the H_∞ norm. The performance conditions are delay independent, and provide convex filtering design problems, which are convex optimization problems with linear matrix inequalities constraints.