Abstract :
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
Keywords :
computational complexity; control system analysis; delays; matrix algebra; robust control; singular value decomposition; uncertain systems; μ analysis; μ upper bound; LMI; LTI systems; NP-hard necessary and sufficient conditions; connected set; linear matrix inequalities; nonrational uncertainties; quadratic constraints; robustness analysis; stability analysis; time-delays; topological separation; uncertain linear time invariant systems; Delay effects; Feedback; Linear matrix inequalities; Robustness; Stability analysis; Sufficient conditions; Time invariant systems; Transfer functions; Uncertainty; Upper bound;
