Abstract
A novel stability analysis for the interval time-delay systems is proposed by employing a new series of integral inequalities for single and double integrals. Different from the recently introduced Wirtinger-based inequalities, refined Jensen inequalities and auxiliary function-based inequalities, the proposed ones can provide more accurate bounds for the cross terms in derivatives of the Lyapunov–Krasovskii functional (LKF) without involving additional slack variables. Based on the augmented LKF with triple-integral terms, their applications to stability analysis for interval time-delay systems are provided. By virtue of the newly derived inequalities, the resulting criteria are less conservative than some existing literature. Finally, numerical examples are provided to verify the effectiveness and improvement of the proposed approaches.
Highlights
Because of the finite speed of data transmission, time delays are unavoidably encountered in a variety of real-world systems, such as multi-agent systems [1,2], active suspension systems [3,4], chemical engineering systems [5], and so on
A considerable amount of attention has been paid to the stability analysis for time-delay systems [8,9,10,11,12,13,14,15]
The reduction of conservatism depends on the construction of Lyapunov–Krasovskii functional (LKF) to a considerable extent, which aims at making use of more information about the delay [11]
Summary
Because of the finite speed of data transmission, time delays are unavoidably encountered in a variety of real-world systems, such as multi-agent systems [1,2], active suspension systems [3,4], chemical engineering systems [5], and so on. A considerable amount of attention has been paid to the stability analysis for time-delay systems [8,9,10,11,12,13,14,15] In this area, the Lyapunov–Krasovskii functional (LKF) is the most efficient mathematical tool [4,5]. In [24], by using Wirtinger-based single and double integral inequalities and delay decomposition technique, the stability analysis of neural systems is investigated. Based on the above discussions, the main contribution of this paper is that a novel series of integral inequalities independent of slack variables is proposed, which shows significant improvements over the Wirtinger-based, refined Jensen and auxiliary function-based ones.
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