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Exponential stabilization of inertial quaternion‐valued Cohen‐Grossberg neural networks: Lexicographical order method
Author(s) -
Li Ruoxia,
Cao Jinde
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.5049
Subject(s) - quaternion , artificial neural network , lexicographical order , interval (graph theory) , control theory (sociology) , equilibrium point , mathematics , uniqueness , controller (irrigation) , class (philosophy) , stability (learning theory) , computer science , artificial intelligence , differential equation , control (management) , mathematical analysis , geometry , combinatorics , agronomy , biology , machine learning
Summary In this article, a general class of delayed interval inertial Cohen‐Grossberg neural networks described by quaternion‐valued parameters is considered. Under the homeomorphism mapping theory and lexicographical order method, we investigate the exponential stabilization problem for the quaternion‐valued Cohen‐Grossberg neural networks. To do so, we verify the existence and uniqueness of the equilibrium point (EP), and then by designing a sampled‐data feedback controller, several sufficient criteria are derived to ascertain the robust stability of the EP for the given system. What should be mentioned is that the state parameters are taking values in an interval, which implies the states are taking values between two different quaternions, thus, a lexicographical order method is employed, which proposed an effective method to determine the “magnitude” of two different quaternions. Finally, numerical example is provided to demonstrate the effectiveness of the developed theoretical results.