Exponential stabilization of inertial quaternion‐valued Cohen‐Grossberg neural networks: Lexicographical order method. (17th June 2020)

• Record Type: Journal Article
• Authors: Li, Ruoxia; Cao, Jinde
• Is Part Of: International journal of robust and nonlinear control. Volume 30:Number 13(2020)
• Page Start: 5205
• Page End: 5220
• Publication Date: 2020-06-17
• Subjects: Cohen‐Grossberg neural networks -- inertial terms -- lexicographical order -- quaternion‐valued -- robust stabilization; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.5049
• Languages: English
• ISSNs: 1049-8923

Abstract

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.