New stability condition for linear systems with time-varying delay

Delay-dependent stabilization problem for a class of linear system with interval time-varying delay is studied. A sufficient condition in terms of linear matrix inequalities (LMIs) is achieved by constructing a novel Lyapunov-Krasovskii functional with the idea of partitioning the time delay, and then using free-weighting matrix approach and adopting inequalities, the interval delay is dealt with successfully. Compared with former stability analysis approaches, this approach can overcome the defect of finding a common positive definite matrix, and reduce conservative greatly. Finally, one simulation example is given to illustrate the effectiveness of the methods.