New Integral Inequality and Its Application to Time-Delay Systems

International audienceIn the last decade, the Jensen’s inequality has been intensively used in the context of time-delay or sampled-data systems since it is an appropriate tool to obtain tractable stability conditions expressed in terms linear matrix inequalities (LMI). However, it is also well-known that this inequality unavoidably introduces an undesirable conservatism in the stability conditions and looking at the literature, reducing this gap is still an open problem. In this paper, we propose an alternative inequality based on the Fourier Theory, more precisely on the Wirtinger’s inequalities. It is showed in this chapter that they allow deriving a new integral inequality which is proved to encompass the Jensen’s inequality. In order to illustrate the potential gain of employing this new inequality with respect to the Jensen’s one, an application to time-delay analysis is provided