A New Slack Lyapunov Functional for Dynamical System with Time Delay

Can Zhao (), Kaibo Shi (), Yiqian Tang and Shouming Zhong
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Can Zhao: School of Information Science and Engineering, Chengdu University, Chengdu 610106, China
Kaibo Shi: School of Information Science and Engineering, Chengdu University, Chengdu 610106, China
Yiqian Tang: School of Information Science and Engineering, Chengdu University, Chengdu 610106, China
Shouming Zhong: School of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China

Mathematics, 2022, vol. 10, issue 23, 1-11

Abstract: The traditional method of constructing a Lyapunov functional for dynamical systems with time delay is usually dependent on positive definite matrices in the quadratic form. In this paper, a new Lyapunov functional is proposed and the corresponding proof is given. It do not require that all matrices in the quadratic form of Lyapunov functionals are positive definite, while the quadratic form is still positive definite, which makes the estimate more relaxed due to special construction of matrices. It is a general form and can be used in the performance analysis of a variety of dynamical systems. Moreover, a lemma concerning the quadratic function is applied to deal with the quadratic term of time-varying delay. Lastly, in the case of classical dynamical systems with time delay, the verification results are given to illustrate the usefulness of the new slack Lyapunov functional.

Keywords: dynamical system; new Lyapunov functional; asymptotic stability; time-varying delays; inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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