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.