Synchronization criteria of delayed inertial neural networks with generally Markovian jumping

Junyi Wang; Zhanshan Wang; Xiangyong Chen; Jianlong Qiu

doi:10.1016/j.neunet.2021.02.004

Synchronization criteria of delayed inertial neural networks with generally Markovian jumping

Neural Netw. 2021 Jul:139:64-76. doi: 10.1016/j.neunet.2021.02.004. Epub 2021 Feb 24.

Authors

Junyi Wang¹, Zhanshan Wang², Xiangyong Chen³, Jianlong Qiu⁴

Affiliations

¹ Faculty of Robot Science and Engineering, Northeastern University, Shenyang, Liaoning, 110819, China; School of Automation and Electrical Engineering, Linyi University, Linyi, Shandong, 276005, China. Electronic address: wangjunyi@mail.neu.edu.cn.
² College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, 110819, China. Electronic address: wangzhanshan@ise.neu.edu.cn.
³ School of Automation and Electrical Engineering, Linyi University, Linyi, Shandong, 276005, China; Key Laboratory of Complex Systems and Intelligent Computing in Universities of Shandong, Linyi University, Linyi, Shandong, 276005, China. Electronic address: chenxiangyong@lyu.edu.cn.
⁴ School of Automation and Electrical Engineering, Linyi University, Linyi, Shandong, 276005, China; Key Laboratory of Complex Systems and Intelligent Computing in Universities of Shandong, Linyi University, Linyi, Shandong, 276005, China. Electronic address: qiujianlong@lyu.edu.cn.

PMID: 33684610
DOI: 10.1016/j.neunet.2021.02.004

Abstract

In this paper, the synchronization problem of inertial neural networks with time-varying delays and generally Markovian jumping is investigated. The second order differential equations are transformed into the first-order differential equations by utilizing the variable transformation method. The Markovian process in the systems is uncertain or partially known due to the delay of data transmission channel or the loss of data information, which is more general and practicable to consider generally Markovian jumping inertial neural networks. The synchronization criteria can be obtained by using the delay-dependent Lyapunov-Krasovskii functionals and higher order polynomial based relaxed inequality (HOPRII). In addition, the desired controllers are obtained by solving a set of linear matrix inequalities. Finally, the numerical examples are provided to demonstrate the effectiveness of the theoretical results.

Keywords: Delay-dependent Lyapunov–Krasovskii functionals; Generally Markovian jumping; Higher order polynomial based relaxed inequality; Inertial neural network.

MeSH terms

Algorithms*
Markov Chains*
Neural Networks, Computer*
Pattern Recognition, Automated / methods*
Time Factors
Uncertainty