Hierarchy of LMI conditions for the stability analysis of time-delay systems

Assessing stability of time-delay systems based on the Lyapunov–Krasovskii functionals has been the subject of many contributions. Most of the results are based, first, on an a priori design of functionals and, finally, on the use of the famous Jensen’s inequality. In contrast with this design process, the present paper aims at providing a generic set of integral inequalities which are asymptotically non conservative and then to design functionals driven by these inequalities. The resulting stability conditions form a hierarchy of LMI which is competitive with the most efficient existing methods (delay-partitioning, discretization and sum of squares), in terms of conservatism and of complexity. Finally, some examples show the efficiency of the method.