Abstract
In the huge literature dedicated to stability of time-delay systems, the most popular approach remains the use of Lyapunov-Krasovskii functionals. This framework allows to study a large class of time-delay systems including constant or time-varying delays. Since several years, the main challenge is to propose new functionals and techniques for deriving less and less conservative stability conditions. Nevertheless, all these approaches usually adopt the same procedure which is based on the well-known Jensen's inequality which generally induces some conservatism difficult to overcome. This paper analyses firstly the conservatism induced by the Jensen's inequality and secondly proposes a wide class of new parametrized inequalities. All these are based on an extensive use of Wirtinger inequality which has been recently introduced in Liu and Fridman [2012] and Seuret and Gouaisbaut [2012b] for stability analysis.
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