Finite-time synchronization of Markovian jump complex networks with generally uncertain transition rates

Abstract

In this paper, finite-time synchronization for a class of Markovian jump complex networks (MJCNs) with generally uncertain transition rates (GUTRs) is considered. In this GUTR network model, each transition rate can be completely unknown or only its estimate value is known. This new uncertain model is more general than partly unknown transition rates (PUTRs). By constructing a suitable stochastic Lyapunov-Krasovskii function, using finitetime stability theorem and pinning control approaches, a sufficient finite-time synchronization criterion is derived in term of linear matrix inequalities (LMIs), which is easy to solve with the help of the LMI toolbox in Matlab. Finally, theoretical results are supported by numerical simulations.

Finite‐Time Synchronization of Uncertain Complex Dynamic Networks with Nonlinear Coupling

“…While regarding the uncertainty and dynamic behavior of a system, the results for a prefunction matrix as a nonidentity matrix are few. In [25,30,32], the uncertainty of a system and the dynamic matrix of the dynamic behavior function were not considered as the identity matrix. A neural network model was used in [34].…”

“…Mei et al [31] discussed a class of finite-time synchronization for drive-response systems with structure identification and uncertain parameters. Xu et al [32] studied the finite-time synchronization of Markovian jump complex networks with generally uncertain transition rates. Ma et al [33] studied the robust and nonfragile finite-time H ∞ synchronization control for complex networks with uncertain inner coupling.…”

“…Zhao et al [34] obtained new results on finite-time parameter identification and synchronization of uncertain complex dynamic networks with perturbations and impulsive effects on the basis of the finite time stability theorem, in which a system's uncertainty is caused by uncertain parameters. Moreover, in [31][32][33][34], the nonlinearity of the internal coupling of systems was not considered. Sun et al [35] realized the finite-time synchronization of complex chaotic systems with three unknown parameter terms by means of sliding mode control.…”

Finite-Time $${H_\infty }$$ H ∞ Synchronization for Complex Dynamical Networks with Markovian Jump Parameter

“…What is more, it is the most important that the synchronization objective is realized in a finite time. Recently, finite-time synchronization for complex networks has been proposed in Wu et al (2015), Jing et al (2015), Mei et al (2013), Zheng et al (2018), Sun et al (2012), Chen et al (2017), Cui et al (2014), Xu et al (2015Xu et al ( , 2016, Li and Cao (2015), Liu et al (2015), Yang and Cao (2010) and Zheng et al (2017). In Cui et al (2014), with Markovian jump complex networks is finite-time synchronization with B Nannan Ma manan0202@163.com 1 School of Science, Southwest Petroleum University, Chengdu 610500, Sichuan, China partially unknown transition rates, by utilizing inequality techniques and the pinning control.…”

“…In Cui et al (2014), with Markovian jump complex networks is finite-time synchronization with B Nannan Ma manan0202@163.com 1 School of Science, Southwest Petroleum University, Chengdu 610500, Sichuan, China partially unknown transition rates, by utilizing inequality techniques and the pinning control. In paper (Xu et al 2015), with Markovian jump complex networks is finite-time synchronization, which each transition rate can be completely unknown or only its estimate value is known. Finite-time synchronization means the optimality in convergence time; in paper (Yang and Cao 2010), finite-time stochastic synchronization of complex networks has been considered, by using finite-time stability theorem, the properties of Weiner process and adding appropriately controllers.…”