Stability analysis of Lur'e systems with additive delay components via a relaxed matrix inequality

Fei Long; Chuan Ke Zhang; Yong He; Lin Jiang; Qing Guo Wang; Min Wu

doi:10.1016/j.amc.2018.01.009

Stability analysis of Lur'e systems with additive delay components via a relaxed matrix inequality

Fei Long, Chuan Ke Zhang, Yong He, Lin Jiang, Qing Guo Wang, Min Wu

Electrical and Electronic Engineering Science

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

38 Citations (Scopus)

Abstract

This paper is concerned with the stability analysis of Lur'e systems with sector-bounded nonlinearity and two additive time-varying delay components. In order to accurately understand the effect of time delays on the system stability, the extended matrix inequality for estimating the derivative of the Lyapunov–Krasovskii functionals (LKFs) is employed to achieve the conservatism reduction of stability criteria. It reduces estimation gap of the popular reciprocally convex combination lemma (RCCL). Combining the extended matrix inequality and two types of LKFs lead to several stability criteria, which are less conservative than the RCCL-based criteria under the same LKFs. Finally, the advantages of the proposed criteria are demonstrated through two examples.

Original language	English
Pages (from-to)	224-242
Number of pages	19
Journal	Applied Mathematics and Computation
Volume	328
DOIs	https://doi.org/10.1016/j.amc.2018.01.009
Publication status	Published - 1 Jul 2018

Keywords

Additive time-varying delays
Linear matrix inequality
Lur'e system
Matrix inequality
Stability

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2018.01.009

Cite this

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title = "Stability analysis of Lur'e systems with additive delay components via a relaxed matrix inequality",

abstract = "This paper is concerned with the stability analysis of Lur'e systems with sector-bounded nonlinearity and two additive time-varying delay components. In order to accurately understand the effect of time delays on the system stability, the extended matrix inequality for estimating the derivative of the Lyapunov–Krasovskii functionals (LKFs) is employed to achieve the conservatism reduction of stability criteria. It reduces estimation gap of the popular reciprocally convex combination lemma (RCCL). Combining the extended matrix inequality and two types of LKFs lead to several stability criteria, which are less conservative than the RCCL-based criteria under the same LKFs. Finally, the advantages of the proposed criteria are demonstrated through two examples.",

keywords = "Additive time-varying delays, Linear matrix inequality, Lur'e system, Matrix inequality, Stability",

author = "Fei Long and Zhang, {Chuan Ke} and Yong He and Lin Jiang and Wang, {Qing Guo} and Min Wu",

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doi = "10.1016/j.amc.2018.01.009",

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T1 - Stability analysis of Lur'e systems with additive delay components via a relaxed matrix inequality

AU - Long, Fei

AU - Zhang, Chuan Ke

AU - He, Yong

AU - Jiang, Lin

AU - Wang, Qing Guo

AU - Wu, Min

PY - 2018/7/1

Y1 - 2018/7/1

N2 - This paper is concerned with the stability analysis of Lur'e systems with sector-bounded nonlinearity and two additive time-varying delay components. In order to accurately understand the effect of time delays on the system stability, the extended matrix inequality for estimating the derivative of the Lyapunov–Krasovskii functionals (LKFs) is employed to achieve the conservatism reduction of stability criteria. It reduces estimation gap of the popular reciprocally convex combination lemma (RCCL). Combining the extended matrix inequality and two types of LKFs lead to several stability criteria, which are less conservative than the RCCL-based criteria under the same LKFs. Finally, the advantages of the proposed criteria are demonstrated through two examples.

AB - This paper is concerned with the stability analysis of Lur'e systems with sector-bounded nonlinearity and two additive time-varying delay components. In order to accurately understand the effect of time delays on the system stability, the extended matrix inequality for estimating the derivative of the Lyapunov–Krasovskii functionals (LKFs) is employed to achieve the conservatism reduction of stability criteria. It reduces estimation gap of the popular reciprocally convex combination lemma (RCCL). Combining the extended matrix inequality and two types of LKFs lead to several stability criteria, which are less conservative than the RCCL-based criteria under the same LKFs. Finally, the advantages of the proposed criteria are demonstrated through two examples.

KW - Additive time-varying delays

KW - Linear matrix inequality

KW - Lur'e system

KW - Matrix inequality

KW - Stability

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DO - 10.1016/j.amc.2018.01.009

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SN - 0096-3003

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EP - 242

JO - Applied Mathematics and Computation

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Stability analysis of Lur'e systems with additive delay components via a relaxed matrix inequality

Abstract

Keywords

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