NDLI: Overview of recent advances in stability of linear systems with time-varying delays

Content Provider	IET Digital Library
Author	Zhang, Xian Ming Han, Qing Long Seuret, Alexandre Gouaisbaut, Frédéric He, Yong
Abstract	This study provides an overview and in-depth analysis of recent advances in stability of linear systems with time-varying delays. First, recent developments of a delay convex analysis approach, a reciprocally convex approach and the construction of Lyapunov–Krasovskii functionals are reviewed insightfully. Second, in-depth analysis of the Bessel–Legendre inequality and some affine integral inequalities is made, and recent stability results are also summarised, including stability criteria for three cases of a time-varying delay, where information on the bounds of the time-varying delay and its derivative is totally known, partly known and completely unknown, respectively. Third, a number of stability criteria are developed for the above three cases of the time-varying delay by employing canonical Bessel–Legendre inequalities, together with augmented Lyapunov–Krasovskii functionals. It is shown through numerical examples that these stability criteria outperform some existing results. Finally, several challenging issues are pointed out to direct the near future research.
Starting Page	1
Ending Page	16
Page Count	16
ISSN	17518644
Volume Number	13
e-ISSN	17518652
Issue Number	Issue 1, Jan (2019)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-cta/13/1
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-cta.2018.5188
Journal	IET Control Theory & Applications
Publisher Date	2018-10-18
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Augmented Lyapunov-Krasovskii Functionals Canonical Bessel–Legendre Inequalities Delay Delay Convex Analysis Approach Delay System Distributed Parameter Control System Linear System Lyapunov Method Reciprocally Convex Approach Stability Criteria Stability in Control Theory Time Varying Control System Time Varying System Time-varying Delay
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Human-Computer Interaction Electrical and Electronic Engineering Computer Science Applications

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