Premium
A sufficient negative‐definiteness condition for cubic functions and application to time‐delay systems
Author(s) -
Long Fei,
Zhang ChuanKe,
He Yong,
Wang QingGuo,
Wu Min
Publication year - 2021
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.5682
Subject(s) - positive definiteness , definiteness , lemma (botany) , positive definite matrix , stability (learning theory) , mathematics , control theory (sociology) , stability criterion , function (biology) , discrete time and continuous time , computer science , control (management) , physics , statistics , ecology , linguistics , eigenvalues and eigenvectors , philosophy , poaceae , quantum mechanics , machine learning , artificial intelligence , evolutionary biology , biology
This article studies the delay‐dependent stability of systems with a time‐varying delay. To get a stability criterion described as linear matrix inequalities (LMIs) from a positive definite Lyapunov‐Krasovskii functional (LKF), the negative‐definiteness condition, guaranteeing the negative definiteness of the derivative of the LKF, is necessary. This article proposes a negative‐definiteness lemma for the cubic function with respect to the time‐varying delay, which achieves the negative‐definiteness requirement without introducing any decision variable and extending the size of the LMIs contained in a stability criterion. Then benefiting from this lemma, an LKF with more delay information is constructed and applied to the stability analysis. After that, a delay‐dependent stability criterion is derived based on the LKF and the negative‐definiteness lemma. Finally, the contribution of the proposed lemma and the stability criterion is demonstrated with two examples.