Robust stability of time-delay systems with interval delays

Stability analysis of uncertain time-delay systems is considered in a quadratic separation framework. Results are formulated in terms of linear matrix inequalities (LMI) which prove to be conservative. But this conservatism is significantly reduced by combining several tools. Firstly, a fractioning of the delay is performed thus introducing knowledge on the functional defining the current state of the system. Secondly, a Taylor series approximation of the delay operator is performed and the Taylor remainder is explicitly taken into account with a new uncertainty-type approximation. Thanks to LMI formulation, and with the use of slack variables, robustness is guaranteed for all uncertainties and all delays included in some bounded interval which may not include zero.