A generalized double integral inequalities approach to stability analysis for time-delay systems

In this paper, the stability analysis for time-delay systems is investigated. Firstly, further improved double integral inequalities in the forms of infinite series are developed for estimation of the derivatives of triple integral terms. Comparing with the recently introduced Wirtinger-based, refined Jensen and auxiliary function-based double integral inequalities, the estimation gaps of the proposed ones are ever-shrinking with increase of the intermediate terms without requiring any free-weighting matrix. Then, by constructing a triple integral type of Lyapunov-Krasovskii functional (LKF), some stability conditions for time-delay systems are established. By virtue of the new inequalities, the derived criteria are less conservative and more computationally attractive than some existing works. Finally, the improvement and effectiveness of the proposed approaches are demonstrated via the numerical examples.