Further results on delay-dependent stability for continuous system with two additive time-varying delay components

Xuemei Yu; Xiaomei Wang; Shouming Zhong; Kaibo Shi

doi:10.1016/j.isatra.2016.08.003

Further results on delay-dependent stability for continuous system with two additive time-varying delay components

ISA Trans. 2016 Nov:65:9-18. doi: 10.1016/j.isatra.2016.08.003. Epub 2016 Aug 24.

Authors

Xuemei Yu¹, Xiaomei Wang¹, Shouming Zhong¹, Kaibo Shi²

Affiliations

¹ School of Mathematical Sciences, University of Electronic Science and Technology of China, Sichuan, China.
² School of Information Science and Engineering, Chengdu University, Chengdu, 610106, China.

PMID: 27568098
DOI: 10.1016/j.isatra.2016.08.003

Abstract

This paper deals with the problem of stability for continuous system with two additive time-varying delay components. By making full use of the information of the marginally delayed state, a novel Lyapunov-Krasovskii functional is constructed. When estimating the derivative of the Lyapunov-Krasovskii functional, we manage to get a fairly tighter upper bound by using the method of reciprocal convex and convex polyhedron. The obtained delay-dependent stability results are less conservative than some existing ones via numerical example comparisons. In addition, this criterion is expressed as a set of linear matrix inequalities, which can be readily tested by using the Matlab LMI toolbox. Finally, four examples are given to illustrate the effectiveness of the proposed method.

Keywords: Additive delay components; Delay-dependent stability; Lyapunov–Krasovskii functional; Time-varying delay.