Pinning exponential synchronisation and passivity of coupled delayed reaction–diffusion neural networks with and without parametric uncertainties

ABSTRACT

In this paper, we focus on the pinning exponential synchronisation and passivity of coupled reaction–diffusion neural networks (CRDNNs) with and without parametric uncertainties, respectively. On the one hand, with the help of designed nonlinear pinning controllers and Lyapunov functional method, sufficient conditions are established to let the CRDNNs with hybrid coupling and mixed time-varying delays realise exponential synchronisation and passivity. On the other hand, considering that the external perturbations may lead the reaction–diffusion neural networks (RDNNs) parameters to containing uncertainties, the robust pinning exponential synchronisation and robust pinning passivity for coupled delayed RDNNs with parametric uncertainties are investigated by designing appropriate pinning control strategies. Finally, the effectiveness of the theoretical results are substantiated by the two given numerical examples.

KEYWORDS:

• Nonlinear pinning controllers
• exponential synchronisation
• robust exponential synchronisation
• passivity
• robust passivity

Acknowledgments

The authors would like to thank the Associate Editor and anonymous reviewers for their valuable comments and suggestions. This work was supported in part by the National Natural Science Foundation of China under Grants 11501411, 61503010, 61403275 and 11401018, in part by the Natural Science Foundation of Tianjin, China, under Grant 15JCQNJC04100, and in part by the Aeronautical Science Foundation of China (No.2016ZA51001).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

National Natural Science Foundation of China [grant number 11501411], [grant number 61503010], [grant number 61403275], [grant number 11401018]; Natural Science Foundation of Tianjin [grant number 15JCQNJC04100]; Aeronautical Science Foundation of China [grant number 2016ZA51001].