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Delay‐Dependent Stability Criterion for Discrete‐Time Systems with Time‐Varying Delays
Author(s) -
Hua Changchun,
Wu Shuangshuang,
Bai Zhenhua,
Guan Xinping
Publication year - 2017
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.1409
Subject(s) - mathematics , stability (learning theory) , discrete time and continuous time , linear matrix inequality , control theory (sociology) , stability criterion , exponential stability , circle criterion , inequality , matrix (chemical analysis) , mathematical optimization , computer science , mathematical analysis , nonlinear system , control (management) , statistics , physics , materials science , quantum mechanics , machine learning , artificial intelligence , composite material
The stability analysis problem is considered for linear discrete‐time systems with time‐varying delays. A novel summation inequality is proposed, which takes the double summation information of the system state into consideration. The inequality relaxes the recently proposed discrete Wirtinger inequality and its improved version. Based on construction of a suitable Lyapunov‐Krasovskii functional and the novel summation inequality, an improved delay‐dependent stability criterion for asymptotic stability of the systems is derived in terms of linear matrix inequalities. Numerical examples are given to demonstrate the advantages of the proposed method.