A note on equivalence between two integral inequalities for time-delay systems

Title: A note on equivalence between two integral inequalities for time-delay systems
Creator: Ji, Xiaofu; Su, Hongye
Relation: Automatica Vol. 53, p. 244-246
Publisher Link: http://dx.doi.org/10.1016/j.automatica.2014.12.030
Publisher: Pergamon
Resource Type: journal article
Date: 2015
Description: Jensen's inequality and extended Jensen's inequality are two important integral inequalities when problems of stability analysis and controller synthesis for time-delay systems are considered. The extended Jensen's inequality introduces two additional free matrices and is generally regarded to be less conservative than Jensen's inequality. The equivalence between Jensen's inequality and extended Jensen's inequality in bounding the quadratic term [formula could not replicated] in Lyapunov functional of time-delay systems is presented and theoretically proved. It is shown that the extended Jensen's inequality does not decrease the lower bound of this quadratic term obtained using Jensen's inequality, and then it does not reduce the conservativeness though two additional free matrices M₁ and M₂ are involved.
Subject: time-delay systems; Jensen's inequality; extended Jensen's inequality; quadratics
Identifier: http://hdl.handle.net/1959.13/1321787
Identifier: uon:24450
Identifier: ISSN:0005-1098
Language: eng
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