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Stability analysis for a class of random nonlinear impulsive systems
Author(s) -
Jiao Ticao,
Zheng Wei Xing,
Xu Shengyuan
Publication year - 2016
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.3630
Subject(s) - nonlinear system , impulse (physics) , uniqueness , mathematics , interval (graph theory) , stability (learning theory) , control theory (sociology) , class (philosophy) , mathematical analysis , computer science , physics , control (management) , combinatorics , classical mechanics , quantum mechanics , machine learning , artificial intelligence
Summary In this paper, the problem of noise‐to‐state stability (NSS) and globally asymptotic stability (GAS) is investigated for a class of nonlinear systems with random disturbances and impulses, where the random noises have finite second‐order moments and the so‐called random impulses mean that impulse ranges are driven by a sequence of random variables. First, some general conditions are given to guarantee the existence and uniqueness of solutions to random nonlinear impulsive systems. Next, when the continuous dynamics are stable but the impulses are destabilizing, the NSS and GAS of random nonlinear impulsive systems are examined by the average impulsive interval approach. Then, when the continuous dynamics are unstable but the impulses are stabilizing, it is shown that the NSS and GAS can be retained by using the reverse average impulsive interval approach. Finally, the theoretical findings are substantiated with illustrative examples. Copyright © 2016 John Wiley & Sons, Ltd.