New delay-derivative-dependent stability criteria for linear systems with interval time-varying delays

This paper is concerned with the delay-derivative-dependent stability analysis for linear systems with interval time-varying delays. First, we divide the whole delay interval into two segmentations with an unequal width and checking the variation of the Lyapunov-Krasovskii functional (LKF) for each subinterval of delay. The relationship between both lower and upper bounds of the delay-derivative have been taken Into account. Unlike the previous methods, the upper bound of the delay derivative is taken into consideration even if this upper bound is larger than or equal to 1. Second, incorporating the delayed-decomposition idea with integral inequality approach (IIA), a new augmented delayed-decomposition LKF is constructed. Third, all the cone itions are presented in terms of linear matrix inequalities (LMIs) can be easily calculated by using Matlab LMI control toolbox. Finally, the numerical examples and the applicatioi to active vibration suppression with time delayed feedback system are provided to verify the effectiveness of the proposed criteria.