Some remarks on the stability of linear systems with delayed state

This paper focuses on `mixed´ delay-independent/delay-dependent asymptotic stability problems of a class of linear systems described by delay-differential equations involving multiple constant delays. Sufficient conditions for characterizing unbounded stability regions in the delays parameter space are given. The proposed approach makes use of some appropriate Liapunov-Krasovskii functionals and the obtained results are expressed in terms of matrix inequalities. Note that these results allow to recover (or to improve) as limit cases previous sufficient delay-independent or/and delay-dependent conditions from the control literature