On the quadratic stability of uncertain systems in the presence of time-delays

This paper considers the problem of quadratic stability of uncertain linear systems. The uncertainty includes a structured one. consisting of unknown but bounded parameter variations (possibly time-dependent), and the presence of unknown distributed time-delays. It is well known that an uncertain system without delays can be stabilized for all parameter variations of a given class by using a so-called "quadratically" stabilizing control law. In the present paper, it is shown that, under a sufficient condition relating the structured uncertainty and the time-delay. that control law stabilizes the delayed system as well.