Stability analysis for linear time-delay systems using new inequality based on the second-order derivative. Issue 15 (October 2019)

• Record Type: Journal Article
• Authors: Zhao, Xin; Lin, Chong; Chen, Bing; Wang, Qing-Guo
• Is Part Of: Journal of the Franklin Institute. Volume 356:Issue 15(2019)
• Page Start: 8770
• Page End: 8784
• Publication Date: 2019-10
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2019.03.038
• Languages: English
• ISSNs: 0016-0032

Abstract

Highlights: A new double integral inequality given in Lemma 4 is proposed based on the second-order derivative of vector functions. Considering the second-order derivative of state, a novel Lyapunov-krasovskii functional is constructed. New delay-dependent stability criteria are given in terms of linear matrix inequality. Numerical examples are given to show the advantages of the proposed methods. Abstract: This paper studies the stability problem of linear time-varying delay system. Firstly, a double integral inequality based on the second-order derivative is proposed in this paper. Secondly, novel Lyapunov–Krasovskii functional consisting of integral terms based on the second-order derivative is constructed to enhance the feasible region of delay-dependent stability. Based on the two aspects, new delay-dependent stability criteria which guarantee the asymptotic stability of linear systems with time-varying delay are given in the form of linear matrix inequality (LMI). Finally, several numerical examples are given to show the advantages of the proposed methods.