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New Augmented Lyapunov‐Krasovskii Functional for Stability Analysis of Systems with Additive Time‐Varying Delays
Author(s) -
Ding Liming,
He Yong,
Wu Min,
Wang Qinggou
Publication year - 2018
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1641
Subject(s) - stability (learning theory) , mathematics , upper and lower bounds , control theory (sociology) , functional approach , derivative (finance) , matrix (chemical analysis) , computer science , mathematical analysis , control (management) , artificial intelligence , materials science , human–computer interaction , machine learning , financial economics , economics , composite material
Abstract This paper is concerned with stability analysis for continuous‐time systems with additive time‐varying delays in the Lyapunov‐Krasovskii(L‐K) framework. Firstly, in view of the relationships between the upper bounds of the two time‐varying delays, a new augmented L‐K functional is constructed by using the information of the two upper bounds. Secondly, the free‐matrix‐based integral inequality is used to estimate the derivative of the constructed L‐K functional. Thirdly, a less conservative criterion is derived to assess stability. Finally, a numerical example is presented to demonstrate the effectiveness of the criterion.