Robustness analysis with time-delays

In this paper, we consider the stability analysis of uncertain linear time invariant systems with several time-delays. The delays are assumed unknown but constant. Working on quadratic constraints within a topological separation framework, we propose an extension of the μ analysis to address the analysis of systems with nonrational uncertainties in a connected set. We obtain (NP hard) necessary and sufficient conditions. Convex sufficient conditions, involving linear matrix inequalities, are then derived. These conditions are an extension of the μ upper bound. Using a conventional μ analysis approach, the obtained conditions would be delay independent or, at least, more conservative than the proposed criterion. We finally evaluate the interest of our conditions on a numerical example