Research Article
Stability Analysis of Quaternion-Valued Neural Network with Non-differentiable Time-Varying Delays and Constant Delays
@INPROCEEDINGS{10.1007/978-3-030-77569-8_18, author={Hongying Qin and Zhenhao Chen and Xiaomei Wang and Guo Huang}, title={Stability Analysis of Quaternion-Valued Neural Network with Non-differentiable Time-Varying Delays and Constant Delays}, proceedings={Quality, Reliability, Security and Robustness in Heterogeneous Systems. 16th EAI International Conference, QShine 2020, Virtual Event, November 29--30, 2020, Proceedings}, proceedings_a={QSHINE}, year={2021}, month={6}, keywords={Quaternion-valued neural network Non-differentiable delays Constant delays Global stability}, doi={10.1007/978-3-030-77569-8_18} }- Hongying Qin
Zhenhao Chen
Xiaomei Wang
Guo Huang
Year: 2021
Stability Analysis of Quaternion-Valued Neural Network with Non-differentiable Time-Varying Delays and Constant Delays
QSHINE
Springer
DOI: 10.1007/978-3-030-77569-8_18
Abstract
The main goal of this paper is to investigate the problems of the uniqueness of equilibrium and the global(\mu )-stability for the QVNN (quaternion-valued neural network) with leaky constant delay, non-differentiable discrete time-varying delay, distributed constant delay, which is closer to practical application than the QVNN with differentiable time-varying delay. Firstly, we discuss the QVNN as entirety, and prove the equilibrium of the QVNN is unique by using Homeomorphism mapping theorem and quaternion-valued linear matrix inequality. Then a new Lyapunov-Krasovskii functional is derived from the delayed state. The sufficient condition of the global(\mu )-stability is given, while appraising the derivative of the Lyapunov-Krasovskii functional and quaternion-valued linear matrix inequality, this result is new and different from the approaches in available literatures. A quaternion-valued numerical example is presented to illustrate these results.
