Global exponential stability in Lagrange sense for quaternion-valued neural networks with leakage delay and mixed time-varying delays

ABSTRACT

This paper deals with the global exponential stability in Lagrange sense for quaternion-valued neural networks (QVNNs) with leakage delay, discrete time-varying delays and distributed delays. By structuring an advisable Lyapunov–Krasovskii functional in quaternion field, and adopting free-weighting-matrix method and inequality technique, a sufficient condition in quaternion-valued linear matrix inequality (LMI) to guarantee the global exponential stability in Lagrange sense is acquired, and the domain of attraction is estimated. A numerical example with simulations is supplied to confirm the availability and feasibility of the raised result.

KEYWORDS:

• Quaternion-valued neural networks
• Lagrange stability
• leakage delay
• discrete time-varying delays
• distributed time-varying delays
• linear matrix inequality

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant no. 61773004], and in part by the Graduate Scientific Research and Innovation Foundation Project of Chongqing [grant nos. CYS17202, CYS18230 and CYB18172], and the Program of Chongqing Innovation Team Project in University [grant no. CXTDX201601022], and the Natural Science Foundation of Chongqing [grant nos. cstc2017jcyjAX0082 and cstc2018jcyjAX0606].