H∞ synchronization of Markov jump neural networks with MPDT switching transition probabilities under DoS attacks

• Published in: Mathematical methods in the applied sciences Vol. 46; no. 14; pp. 15412 - 15425
• Main Authors: Wang, Xiaomin, Li, Feng, Shen, Hao, Wang, Jing
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 30.09.2023
• Subjects: Control systems design; Controllers; Criteria; Denial of service attacks; DoS attacks; H-infinity control; Markov chains; Markov jump neural networks; mode‐dependent persistent dwell‐time switching rule; Neural networks; Switching; synchronization control; Time synchronization; Transition probabilities
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.9386

In this paper, the H∞$$ {H}_{\infty } $$ synchronization issue of discrete‐time Markov jump neural networks under DoS attacks is studied, in which the transition probability of the Markov chain is considered as time‐varying governed by a mode‐dependent persistent dwell‐time switching rule. The purpose of this paper is to design a suitable controller such that mean‐square exponentially stable of the synchronization error system can be accomplished, and an H∞$$ {H}_{\infty } $$ performance is satisfied under denial of service (DoS) attacks. In order to reduce the conservatism of obtained results, some synchronization analysis criteria are obtained by adopting an activation function division method. Based on these criteria, an effective security synchronization controller design method is presented. Conclusively, an example is given to verify the validity of the results.