$Finite-gain L ∞ $\mathcal{L_{\infty}}$ stability from disturbance to output of a class of time delay system$

Finite-gain L ∞ $\mathcal{L_{\infty}}$ stability from disturbance to output of a class of time delay system

Abstract Results on finite-gain L ∞ $\mathcal{L_{\infty}}$ stability from a disturbance to the output of a time-variant delay system are presented via a delay decomposition approach. By constructing an appropriate Lyapunov-Krasovskii functional and a novel integral inequality, which gives a tighter...

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Main Authors:	Ping Li, Xinzhi Liu, Wu Zhao
Format:	Article
Language:	English
Published:	SpringerOpen 2017-01-01
Series:	Journal of Inequalities and Applications
Subjects:	finite-gain L ∞ $\mathcal{L_{\infty}}$ stable from disturbance to output Lyapunov-Krasovskii functional delay decomposition method time-variant delay
Online Access:	http://link.springer.com/article/10.1186/s13660-016-1290-y

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spelling	doaj-299c00d737224e30bc6fba4196bb55692020-11-25T00:50:09ZengSpringerOpenJournal of Inequalities and Applications1029-242X2017-01-012017111810.1186/s13660-016-1290-yFinite-gain L ∞ $\mathcal{L_{\infty}}$ stability from disturbance to output of a class of time delay systemPing Li0Xinzhi Liu1Wu Zhao2College of Computer Science and Technology, Southwest University for NationalitiesDepartment of Applied Mathematics, University of WaterlooSchool of Management and Economics, University of Electronic Science and Technology of ChinaAbstract Results on finite-gain L ∞ $\mathcal{L_{\infty}}$ stability from a disturbance to the output of a time-variant delay system are presented via a delay decomposition approach. By constructing an appropriate Lyapunov-Krasovskii functional and a novel integral inequality, which gives a tighter upper bound than Jensen’s inequality and Bessel-Legendre inequality, some sufficient conditions are established and desired feedback controllers are designed in terms of the solution to certain LMIs. Compared with the existing results, the obtained criteria are more effective due to the tuning scalars and free-weighting matrices. Numerical examples and their simulations are given to demonstrate the effectiveness of the proposed method.http://link.springer.com/article/10.1186/s13660-016-1290-yfinite-gain L ∞ $\mathcal{L_{\infty}}$ stable from disturbance to outputLyapunov-Krasovskii functionaldelay decomposition methodtime-variant delay
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Ping Li Xinzhi Liu Wu Zhao
spellingShingle	Ping Li Xinzhi Liu Wu Zhao Finite-gain L ∞ $\mathcal{L_{\infty}}$ stability from disturbance to output of a class of time delay system Journal of Inequalities and Applications finite-gain L ∞ $\mathcal{L_{\infty}}$ stable from disturbance to output Lyapunov-Krasovskii functional delay decomposition method time-variant delay
author_facet	Ping Li Xinzhi Liu Wu Zhao
author_sort	Ping Li
title	Finite-gain L ∞ $\mathcal{L_{\infty}}$ stability from disturbance to output of a class of time delay system
title_short	Finite-gain L ∞ $\mathcal{L_{\infty}}$ stability from disturbance to output of a class of time delay system
title_full	Finite-gain L ∞ $\mathcal{L_{\infty}}$ stability from disturbance to output of a class of time delay system
title_fullStr	Finite-gain L ∞ $\mathcal{L_{\infty}}$ stability from disturbance to output of a class of time delay system
title_full_unstemmed	Finite-gain L ∞ $\mathcal{L_{\infty}}$ stability from disturbance to output of a class of time delay system
title_sort	finite-gain l ∞ $\mathcal{l_{\infty}}$ stability from disturbance to output of a class of time delay system
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1029-242X
publishDate	2017-01-01
description	Abstract Results on finite-gain L ∞ $\mathcal{L_{\infty}}$ stability from a disturbance to the output of a time-variant delay system are presented via a delay decomposition approach. By constructing an appropriate Lyapunov-Krasovskii functional and a novel integral inequality, which gives a tighter upper bound than Jensen’s inequality and Bessel-Legendre inequality, some sufficient conditions are established and desired feedback controllers are designed in terms of the solution to certain LMIs. Compared with the existing results, the obtained criteria are more effective due to the tuning scalars and free-weighting matrices. Numerical examples and their simulations are given to demonstrate the effectiveness of the proposed method.
topic	finite-gain L ∞ $\mathcal{L_{\infty}}$ stable from disturbance to output Lyapunov-Krasovskii functional delay decomposition method time-variant delay
url	http://link.springer.com/article/10.1186/s13660-016-1290-y
work_keys_str_mv	AT pingli finitegainlmathcallinftystabilityfromdisturbancetooutputofaclassoftimedelaysystem AT xinzhiliu finitegainlmathcallinftystabilityfromdisturbancetooutputofaclassoftimedelaysystem AT wuzhao finitegainlmathcallinftystabilityfromdisturbancetooutputofaclassoftimedelaysystem
_version_	1725249064901017600

Finite-gain L ∞ $\mathcal{L_{\infty}}$ stability from disturbance to output of a class of time delay system

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