Delay-dependent stability analysis of time-delay systems by utilizing a new integral inequality and delay-decomposition approach

This article addressed the problem of delay-dependent stability criteria for linear time system with interval time-delay. Firstly, we proposed a new inequality based on the Fourier Theory, more precisely on the Wirtingers inequalities, which is proved to encompass the Jensens inequality. Secondly, a less conservative stability condition is established in terms of linear matrix inequalities by employing delay-partition idea and Lyapunov functional method. Finally, in order to illustrate the potential gain of employing this new inequality with respect to the Jensens one and the effectiveness of the proposed results,an application to time-delay analysis is provided.