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Anti-periodic Synchronization of Quaternion-valued Generalized Cellular Neural Networks with Time-varying Delays and Impulsive Effects

Yongkun Li*, Yanchao Fang, and Jiali Qin
International Journal of Control, Automation, and Systems, vol. 17, no. 5, pp.1191-1208, 2019

Abstract : "In this paper, a class of quaternion-valued generalized cellular neural networks (QVGCNNs) with timevarying delays and impulsive effects is considered. Firstly, by constructing an appropriate Lyapunov function and applying inequality techniques, some sufficient conditions on the existence of anti-periodic solutions are established. Then, the global exponential anti-periodic synchronization of delayed QVGCNNs with impulsive effects and anti-periodic coefficients is investigated by designing a novel nonlinear state-feedback controller and constructing suitable Lyapunov functions. Our results are completely new even if the considered quaternion-valued systems degenerated into real-valued or complex-valued systems. Finally, two numerical examples are given to illustrate the feasibility and effectiveness of the obtained results"

Keyword : Anti-periodic solution, generalized cellular neural network, quaternion, synchronization.

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