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A unified criterion for global exponential stability of quaternion‐valued neural networks with hybrid impulses
Author(s) -
Ji Xinrui,
Lu Jianquan,
Lou Jungang,
Qiu Jianlong,
Shi Kaibo
Publication year - 2020
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.5210
Subject(s) - quaternion , exponential stability , mathematics , control theory (sociology) , impulse (physics) , artificial neural network , stability (learning theory) , convergence (economics) , stability criterion , interval (graph theory) , norm (philosophy) , representation (politics) , exponential function , computer science , mathematical analysis , geometry , artificial intelligence , physics , control (management) , quantum mechanics , nonlinear system , machine learning , statistics , discrete time and continuous time , combinatorics , politics , political science , law , economics , economic growth
Summary In this article, the stability of quaternion‐valued neural networks (QVNNs) with hybrid impulses is investigated, which contain stabilizing impulses and destabilizing impulses simultaneously. Through constructing the relationship between impulses and quaternions, this article has obtained a unified criterion for the global exponential stability of the system. First, a new form of impulsive representation is constructed, and the established systems can be decomposed into four different real parts. According to the characteristics of the impulses, the system divides the average interval of impulses (AII) into two cases, that is,T α < ∞ andT α = ∞ , which can process hybrid impulses simultaneously. Second, for QVNNs, by using the method of matrix p ‐norm and the inequality technology, the criterion of each interval is derived. Considering the impulsive effects on the overall stability of QVNNs, the uniform criterion for the global exponential stability can be obtained. In addition, the convergence rate of QVNNs with hybrid impulses is also discussed. Finally, in order to verify the theoretical conclusions, some numerical simulations are given.