Novel Stability Criteria for Linear Time-Delay Systems Using Lyapunov-Krasovskii Functionals With A Cubic Polynomial on Time-Varying Delay

Xian-Ming Zhang; Qing-Long Han; Xiaohua Ge

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Novel Stability Criteria for Linear Time-Delay Systems Using Lyapunov-Krasovskii Functionals With A Cubic Polynomial on Time-Varying Delay

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One of challenging issues on stability analysis of time-delay systems is how to obtain a stability criterion from a matrix-valued polynomial on a time-varying delay.The first contribution of this paper is to establish a necessary and sufficient condition on a matrix-valued polynomial inequality over a certain closed interval.The degree of such a matrix-valued polynomial can be an arbitrary finite positive integer.The second contribution of this paper is to introduce a novel LyapunovKrasovskii functional,which includes a cubic polynomial on a time-varying delay,in stability analysis of time-delay systems.Based on the novel Lyapunov-Krasovskii functional and the necessary and sufficient condition on matrix-valued polynomial inequalities,two stability criteria are derived for two cases of the time-varying delay.A well-studied numerical example is given to show that the proposed stability criteria are of less conservativeness than some existing ones.

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《自动化学报：英文版》 |2021年第1期|P.77-85|共9页
作者
Xian-Ming Zhang; Qing-Long Han; Xiaohua Ge;
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作者单位

the School of Software and Electrical Engineering Swinburne University of Technology Melbourne VIC 3122 Australia;

the School of Software and Electrical Engineering Swinburne University of Technology Melbourne VIC 3122 Australia;

the School of Software and Electrical Engineering Swinburne University of Technology Melbourne VIC 3122 Australia;

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原文格式 PDF
正文语种 chi
中图分类数学分析;
关键词
Bessel-Legendre inequality; matrix-valued polynomial inequalities; stability; time-varying delay; time-delay systems;

机译：Bessel-Legendre不等式;矩阵值多项式不等式;稳定性;时变延迟;时间延迟系统;

Novel Stability Criteria for Linear Time-Delay Systems Using Lyapunov-Krasovskii Functionals With A Cubic Polynomial on Time-Varying Delay

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