New results on stability analysis of delayed systems derived from extended wirtinger's integral inequality

This work is concerned with the stability analysis of continuous systems with interval time-varying delays. Novel delay-dependent and delay-rate-dependent stability criteria in terms of linear matrix inequalities (LMIs) are established, which is made possible by: (i) an extended Wirtinger's integral inequality which includes the celebrated Wirtinger-based integral inequality as a special case and delivers more accurate lower bounds than the latter does; (ii) a type of new augmented Lyapunov-Krasovskii functional (LKF) where all possible information of the delay such as its lower, upper bounds, upper bound of its derivative and the relationship among a current state, an exactly delayed state, marginally delayed states are fully exploited; and (iii) transforming the upper bounds of the derivative of the LKF into an affine function concerning the delay. The developed stability conditions for systems with time-varying delays are less conservative as compared with most existing ones. Numerical examples authenticate the effectiveness and improvement of the proposed method over existing results. (C) 2017 Elsevier B.V. All rights reserved.