ℋ_∞/passive non-fragile synchronisation of Markovian jump stochastic complex dynamical networks with time-varying delays

Abstract

This paper deals with the problem of /passive non-fragile synchronisation for a class of complex dynamical networks subject to Markovian jumping time-varying coupling delays. Gain variation is represented by a stochastic variable that is assumed to satisfy the Bernoulli distribution with white sequences. The synchronisation error system became stable through our designed controller. By Lyapunov–Krasovskii stability theory, a new stochastic synchronisation criterion is established for the considered network in terms of linear matrix inequality (LMI). An illustration is given to show effectiveness of the proposed theoretical results.

Keywords:

• Synchronization
• complex dynamical networks
• non-fragile control
• Markov jump parameters
• stochastic noise
• time-varying delays

Disclosure statement

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

Additional information

Funding

This work is supported by NBHM [grant number 2—48(5)/2016/NBHMR.P/-R-D II/14088], and the Jiangsu Provincial Key Laboratory of Networked Collective Intelligence [grant number BM2017002]. The work of O.M. Kwon was supported in part by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education [grant number NRF-2019R1I1A3A02058096], [grant number NRF-2020R1A6A1-A12047945], in part by the Brain Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning [grant number NRF-2017M3C7A1044815] and in part by the MSIT (Ministry of Science and ICT), Korea, under the ITRC (Information Technology Research Center) support program [grant number IITP-2020-1711120023] supervised by the IITP (Institute for Information & Communications Technology Planning & Evaluation).