Stability analysis of linear systems with two additive time-varying delays via delay-product-type Lyapunov functional



Xu, Hao-Tian, Zhang, Chuan-Ke, Jiang, Lin ORCID: 0000-0001-6531-2791 and Smith, Jeremy ORCID: 0000-0002-0212-2365
(2017) Stability analysis of linear systems with two additive time-varying delays via delay-product-type Lyapunov functional. APPLIED MATHEMATICAL MODELLING, 45. pp. 955-964.

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Abstract

This paper is concerned with the stability analysis of continuous linear systems with two additive time-varying delays in the Lyapunov–Krasovskii functional (LKF) framework. Two novel delay-product-type terms are introduced into LKF candidate inspired by our previous research. The Wirtinger-based inequality, together with the reciprocally convex combination technique, is applied to estimate the integral terms arising in the derivative of the LKF. As a result, a new delay- and its-change-rate-dependent stability criterion is established. Its advantage of less conservatism than some existing criteria is demonstrated through a numerical example. Finally, the stability criterion is applied to analyze the stability of the load frequency control scheme of power systems.

Item Type: Article
Additional Information: publisher: Elsevier articletitle: Stability analysis of linear systems with two additive time-varying delays via delay-product-type Lyapunov functional journaltitle: Applied Mathematical Modelling articlelink: http://dx.doi.org/10.1016/j.apm.2017.01.032 content_type: article copyright: © 2017 Elsevier Inc. All rights reserved.
Uncontrolled Keywords: Linear system, Time-varying delay, Stability, Writinger-based inequality, Delay-product-type functional
Depositing User: Symplectic Admin
Date Deposited: 10 Apr 2017 06:51
Last Modified: 03 Feb 2023 02:59
DOI: 10.1016/j.apm.2017.01.032
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3006857