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Stability of impulsive coupled systems on networks with both multicoupling structure and time‐varying delays
Author(s) -
Wang Pengfei,
Sun Zhenyao,
Fan Meng,
Su Huan
Publication year - 2019
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.4499
Subject(s) - stability (learning theory) , control theory (sociology) , nonlinear system , computer science , coupling (piping) , digraph , bidirectional associative memory , artificial neural network , content addressable memory , lyapunov function , topology (electrical circuits) , mathematics , control (management) , physics , artificial intelligence , engineering , discrete mathematics , mechanical engineering , quantum mechanics , machine learning , combinatorics
Summary This paper explores the stability of impulsive coupled systems on networks with both multicoupling structure and time‐varying delays (ICSNMT). The coupling structure can be nonlinear and the time‐varying delays in which can be different, which can well describe more realistic networks. In order to describe this multicoupling structure, we build ICSNMT on a digraph with multiple arcs. Two cases are discussed, ie, (i) the continuous dynamics is stable and (ii) the impulsive dynamics is stable. Then, by means of impulsive differential inequalities with multiple delays and weighted Lyapunov functions method where the weights are closely linked to the network's topological structure, some stability criteria are established. Then, the theoretical results are illustrated by examples of bidirectional associative memory neural networks and coupled modified Chua's circuits, respectively. The numerical simulations are also carried out to demonstrate the effectiveness and feasibility of our theoretical findings.