Stability of time-delay systems with non-small delay

This paper is dedicated to the stability of linear time-delay system for a non small delay h. This is motivated by the fact that in some cases introducing a delay in the loop may stabilize a system. Compared to previously derived results the methodology is totally new and the resulting LMI formulas are original contributions. The derived criteria are based on Taylor series of the delay operator for which the Lagrange remainder is treated as a bounded uncertainty. A sequence of results with decreasing conservatism are obtained applying quadratic separation. An extension to robust analysis with respect to uncertain delay is also derived. A numerical example illustrates the efficiency