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Novel delay‐derivative‐dependent stability criteria using new bounding techniques
Author(s) -
Zhang XianMing,
Han QingLong
Publication year - 2012
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.2829
Subject(s) - bounding overwatch , stability (learning theory) , circle criterion , mathematics , interval (graph theory) , stability criterion , derivative (finance) , upper and lower bounds , control theory (sociology) , regular polygon , stability conditions , exponential stability , computer science , nonlinear system , mathematical analysis , statistics , artificial intelligence , physics , geometry , discrete time and continuous time , control (management) , quantum mechanics , machine learning , combinatorics , financial economics , economics
SUMMARY This paper studies the stability of linear systems with interval time‐varying delays. By constructing a new Lyapunov–Krasovskii functional, two delay‐derivative‐dependent stability criteria are formulated by incorporating with two different bounding techniques to estimate some integral terms appearing in the derivative of the Lyapunov–Krasovskii functional. The first stability criterion is derived by using a generalized integral inequality, and the second stability criterion is obtained by employing a reciprocally convex approach. When applying these two stability criteria to check the stability of a linear system with an interval time‐varying delay, it is shown through some numerical examples that the first stability criterion can provide a larger upper bound of the time‐varying delay than the second stability criterion. Copyright © 2012 John Wiley & Sons, Ltd.