New Augmented Lyapunov-Krasovskii Functional for Stability Analysis of Systems with Additive Time-Varying Delays

Liming Ding; Yong He; Min Wu; Qinggou Wang

doi:10.1002/asjc.1641

New Augmented Lyapunov-Krasovskii Functional for Stability Analysis of Systems with Additive Time-Varying Delays

Liming Ding, Yong He, Min Wu, Qinggou Wang

Electrical and Electronic Engineering Science

Research output: Contribution to journal › Article › peer-review

25 Citations (Scopus)

Abstract

This paper is concerned with stability analysis for continuous-time systems with additive time-varying delays in the Lyapunov-Krasovskii(L-K) framework. Firstly, in view of the relationships between the upper bounds of the two time-varying delays, a new augmented L-K functional is constructed by using the information of the two upper bounds. Secondly, the free-matrix-based integral inequality is used to estimate the derivative of the constructed L-K functional. Thirdly, a less conservative criterion is derived to assess stability. Finally, a numerical example is presented to demonstrate the effectiveness of the criterion.

Original language	English
Pages (from-to)	1663-1670
Number of pages	8
Journal	Asian Journal of Control
Volume	20
Issue number	4
DOIs	https://doi.org/10.1002/asjc.1641
Publication status	Published - Jul 2018

Keywords

Lyapunov-Krasovskii (L-K) functional
additive time-varying delays
free-matrix-based integral inequality
linear matrix inequalities (LMIs)

ASJC Scopus subject areas

Electrical and Electronic Engineering
Control and Systems Engineering
Mathematics (miscellaneous)

Access to Document

10.1002/asjc.1641

Cite this

@article{e246c7c486bc45178d45a686b6e6101b,

title = "New Augmented Lyapunov-Krasovskii Functional for Stability Analysis of Systems with Additive Time-Varying Delays",

abstract = "This paper is concerned with stability analysis for continuous-time systems with additive time-varying delays in the Lyapunov-Krasovskii(L-K) framework. Firstly, in view of the relationships between the upper bounds of the two time-varying delays, a new augmented L-K functional is constructed by using the information of the two upper bounds. Secondly, the free-matrix-based integral inequality is used to estimate the derivative of the constructed L-K functional. Thirdly, a less conservative criterion is derived to assess stability. Finally, a numerical example is presented to demonstrate the effectiveness of the criterion.",

keywords = "Lyapunov-Krasovskii (L-K) functional, additive time-varying delays, free-matrix-based integral inequality, linear matrix inequalities (LMIs)",

author = "Liming Ding and Yong He and Min Wu and Qinggou Wang",

note = "Publisher Copyright: {\textcopyright} 2017 Chinese Automatic Control Society and John Wiley \& Sons Australia, Ltd",

year = "2018",

month = jul,

doi = "10.1002/asjc.1641",

language = "English",

volume = "20",

pages = "1663--1670",

journal = "Asian Journal of Control",

issn = "1561-8625",

publisher = "Wiley-Blackwell",

number = "4",

}

TY - JOUR

T1 - New Augmented Lyapunov-Krasovskii Functional for Stability Analysis of Systems with Additive Time-Varying Delays

AU - Ding, Liming

AU - He, Yong

AU - Wu, Min

AU - Wang, Qinggou

PY - 2018/7

Y1 - 2018/7

N2 - This paper is concerned with stability analysis for continuous-time systems with additive time-varying delays in the Lyapunov-Krasovskii(L-K) framework. Firstly, in view of the relationships between the upper bounds of the two time-varying delays, a new augmented L-K functional is constructed by using the information of the two upper bounds. Secondly, the free-matrix-based integral inequality is used to estimate the derivative of the constructed L-K functional. Thirdly, a less conservative criterion is derived to assess stability. Finally, a numerical example is presented to demonstrate the effectiveness of the criterion.

AB - This paper is concerned with stability analysis for continuous-time systems with additive time-varying delays in the Lyapunov-Krasovskii(L-K) framework. Firstly, in view of the relationships between the upper bounds of the two time-varying delays, a new augmented L-K functional is constructed by using the information of the two upper bounds. Secondly, the free-matrix-based integral inequality is used to estimate the derivative of the constructed L-K functional. Thirdly, a less conservative criterion is derived to assess stability. Finally, a numerical example is presented to demonstrate the effectiveness of the criterion.

KW - Lyapunov-Krasovskii (L-K) functional

KW - additive time-varying delays

KW - free-matrix-based integral inequality

KW - linear matrix inequalities (LMIs)

UR - https://www.scopus.com/pages/publications/85050556360

U2 - 10.1002/asjc.1641

DO - 10.1002/asjc.1641

M3 - Article

AN - SCOPUS:85050556360

SN - 1561-8625

VL - 20

SP - 1663

EP - 1670

JO - Asian Journal of Control

JF - Asian Journal of Control

IS - 4

ER -

New Augmented Lyapunov-Krasovskii Functional for Stability Analysis of Systems with Additive Time-Varying Delays

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this