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Interval stability and interval stabilization of linear stochastic systems with time‐varying delay
Author(s) -
Zhang Huasheng,
Xia Jianwei,
Park Ju H.,
Sun Wei,
Zhuang Guangming
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.5408
Subject(s) - interval (graph theory) , stability (learning theory) , control theory (sociology) , circle criterion , mathematics , stability criterion , convergence (economics) , nonlinear system , exponential stability , computer science , control (management) , discrete time and continuous time , statistics , physics , combinatorics , machine learning , artificial intelligence , quantum mechanics , economics , economic growth
This article first investigates the criterion of interval stability for linear stochastic systems with time‐varying delay via equivalent systems and Lyapunov–Krasovskii (L‐K) functionals. Different from existing stability conditions, the criterion of interval stability can be used to make a more accurate judgment of the stability for linear time‐delay systems. In other words, the new criterion can judge not only the stability of the system but also the speed of its convergence. Meanwhile, based on the criterion of the interval stability, the condition of interval stabilization is derived, which cannot only ensure the stability of the linear time‐delay systems, but also adjust the convergence rate of the states to the ideal level. A numerical instance is presented to illustrate the advantages of the resulting interval stabilization criterion.