NDLI: New stability criterion using a matrix-based quadratic convex approach and some novel integral inequalities

Content Provider	IET Digital Library
Author	Zhang, Xian Ming Han, Qing Long
Abstract	This study is concerned with the stability of a linear system with an interval time-varying delay. First, a new augmented Lyapunov–Krasovskii functional (LKF) is constructed, which includes three integral terms in the form of ∫ t−h t (h−t)+)s) j ẋ T R j ẋ (s) ds (j)=) 1, 2, 3). Second, three novel integral inequalities are established to estimate the upper bounds of the integrals ∫ t−h t (h−t)+)s) j ẋ T R j ẋ (s) ds (j)=) 0, 1, 2) appearing in the derivative of the LKF. Third, a matrix-based quadratic convex approach is introduced to prove not only the negative definiteness of the derivative of the LKF along with the trajectory of the system, but also the positive definiteness of the LKF. Finally, a novel delay-derivative-dependent stability criterion is formulated. The effectiveness of the stability criterion is shown through two numerical examples.
Starting Page	1054
Ending Page	1061
Page Count	8
ISSN	17518644
Volume Number	8
e-ISSN	17518652
Issue Number	Issue 12, Aug (2014)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-cta/8/12
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-cta.2013.0840
Journal	IET Control Theory & Applications
Publisher Date	2014-05-20
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Algebra Augmented Lyapunov-Krasovskii Functional Convex Programming Delay Derivative Dependent Stability Criterion Integral Equation Integral Term Interval Time-varying Delay Linear System LKF Mathematical Analysis Matrix Algebra Matrix-based Quadratic Convex Approach Novel Integral Inequalities Optimisation Technique Positive Definiteness Quadratic Programming Stability Stability in Control Theory
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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