Stability and stabilization of quaternion-valued neural networks with uncertain time-delayed impulses: Direct quaternion method

Zhengwen Tu, Xinsong Yang, Liangwei Wang and Nan Ding

Physica A: Statistical Mechanics and its Applications, 2019, vol. 535, issue C

Abstract: In this paper, the exponential stability of impulsive quaternion-valued neural networks (IQVNNs) with time delays is investigated. Both the differential equation and impulses are affected by time-varying delays which may be nonidentical. Uncertain parameters in impulses are also considered. Firstly, the existence and uniqueness of the equilibrium of the IQVNNs are discussed with the help of homeomorphic mapping theorem. Then, by utilizing Lyapunov functions and a newly developed inequality, several sufficient criteria are established in the form of quaternion-valued linear matrix inequalities (LMIs). It should be noted that, compared to most of existing results which are obtained by decomposing quaternion-valued neural networks (QVNNs) into four real-valued neural networks (RVNNs) or two complex-valued neural networks (CVNNs), our results are easier to be verified since the quaternion-valued LMIs exhibit lower dimensions. Then, based on obtained results, one impulsive controller is designed to realize the stabilization of delayed QVNNs. Finally, two numerical examples are presented to verify the effectiveness and merits of the theoretical analysis.

Keywords: Quaternion-valued neural networks (QVNNs); Impulse delay; Stability; Impulsive control (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437119313585
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:535:y:2019:i:c:s0378437119313585

DOI: 10.1016/j.physa.2019.122358

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().