Dissipativity of the stochastic Markovian switching CVNNs with randomly occurring uncertainties and general uncertain transition rates

Abstract

The robust dissipativity problem is analysed in this article for the Markovian switching complex-valued neural networks perturbed by stochastic noises, where the transition rates of the Markovian switching are uncertain which comprise two categories: completely unknown or unknown but with known upper/lower bounds. The randomly occurring system uncertainties are governed by certain mutually independent Bernoulli-distributed white sequences, which might reflect more realistic dynamical behaviours of the switching network. Based on the generalised It$\hat{o}$'s formula in complex form as well as certain stochastic analysis methods, several mode-dependent dissipativity/passivity criteria are obtained in terms of complex matrix inequalities. Finally, illustrative examples are provided to demonstrate feasibility of the derived results.

Keywords:

• Complex-valued neural networks
• dissipativity
• Markovian switching
• general uncertain transition rates
• stochastic disturbances
• randomly occurring uncertainties

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by the National Key Research and Development Program of China [grant number 2018AAA0100202]; the National Natural Science Foundation of China [grant number 61673110], [grant number 61833005]; the Jiangsu Provincial Key Laboratory of Networked Collective Intelligence [grant number BM2017002]; and the Scientific Research Foundation of Graduate School of Southeast University [grant number YBPY1870].

Notes on contributors

Qiang Li

Qiang Li received the B.Sc. degree in mathematics from Changzhi University, Changzhi, China, in 2014, and the M.Sc. degree in operational research and cybernetics from North Minzu University, Yinchuan, China, in 2017. From 2017, he is pursuing the Ph.D. degree from Southeast University, Nanjing, China. His research interests include complex networks and complex-valued neural networks.

Jinling Liang

Jinling Liang received the B.Sc. and M.Sc. degrees in mathematics from Northwest University, Xi'an, China, in 1997 and 1999, respectively, and the Ph.D. degree in applied mathematics from Southeast University, Nanjing, China, in 2006. She is currently a Professor in the School of Mathematics, Southeast University. She has published around 90 papers in refereed international journals. Her current research interests include stochastic systems, complex networks, robust filtering and bioinformatics.