Improved delay-range-dependent stability for linear systems with time-varying delays based on affine function

In this brief, the problem of stability for linear systems with interval time-varying delays is investigated. A type of new augmented Lyapunov-Krasovskii functional (LKFs) are constructed where more information of delay and some triple-integral terms are included. By our lemmas and others bounded techniques, the upper bound of derivative of the proposed LKFs can be expressed as an affine function with respect to the delay. Based on property of the affine function, improved delay-range dependent stability criteria with less conservative are derived in terms of linear matrix inequalities (LMIs). Numerical examples authenticate the effectiveness of the proposed method.