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New absolute stability results for Lurie systems with interval time‐varying delay based on improved Wirtinger‐type integral inequality
Author(s) -
Zhang Liansheng,
Wang Shuxia,
Yu Wei,
Song Yongduan
Publication year - 2019
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.4526
Subject(s) - bounding overwatch , mathematics , interval (graph theory) , control theory (sociology) , bounded function , stability (learning theory) , nonlinear system , upper and lower bounds , derivative (finance) , convergence (economics) , control (management) , mathematical analysis , computer science , combinatorics , physics , quantum mechanics , artificial intelligence , machine learning , economics , economic growth , financial economics
Summary This work focuses on the absolute stability problem of Lurie control system with interval time‐varying delay and sector‐bounded nonlinearity. Firstly, we present a refined Wirtinger's integral inequality and establish an improved Wirtinger‐type double integral inequality. Secondly, a modified augmented Lyapunov‐Krasovskii functional (LKF) is constructed to analyze the stability of Lurie system, where the information on the lower and upper bounds of the delay and the delay itself are fully exploited. Based on the proposed integral inequalities and some bounding techniques, the upper bound of the derivative of the LKF can be estimated more tightly. Accordingly, the proposed absolute stability criteria, formulated in terms of linear matrix inequalities, are less conservative than those in previous literature. Finally, numerical examples demonstrate the effectiveness and advantage of the proposed method.