Stability analysis for linear time-delay systems using new inequality based on the second-order derivative. Issue 15 (October 2019) - Zhao, Xin; Lin, Chong; Chen, Bing; Wang, Qing-Guo
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.