Finite‐Time Nonfragile Synchronization of Stochastic Complex Dynamical Networks with Semi‐Markov Switching Outer Coupling

Abstract

The problem of robust nonfragile synchronization is investigated in this paper for a class of complex dynamical networks subject to semi-Markov jumping outer coupling, time-varying coupling delay, randomly occurring gain variation, and stochastic noise over a desired finite-time interval. In particular, the network topology is assumed to follow a semi-Markov process such that it may switch from one to another at different instants. In this paper, the random gain variation is represented by a stochastic variable that is assumed to satisfy the Bernoulli distribution with white sequences. Based on these hypotheses and the Lyapunov-Krasovskii stability theory, a new finite-time stochastic synchronization criterion is established for the considered network in terms of linear matrix inequalities. Moreover, the control design parameters that guarantee the required criterion are computed by solving a set of linear matrix inequality constraints. An illustrative example is finally given to show the effectiveness and advantages of the developed analytical results.

Synchronization in pth Moment for Stochastic Chaotic Neural Networks with Finite‐Time Control

“…At present, some authors studied the finitetime stability of stochastic neural networks [15,16], and some authors discussed the pth moment stability of stochastic neural networks [11,[17][18][19]. In these studies, LMI and a matrix equality constraint conditions often were applied to establish sufficient conditions about finite-time mean square asymptotic stability of the stochastic neural network [20][21][22][23]. As the LMI software cannot handle large-sized problems and it is not numerically stable, adaptive finite-time control method can be more useful for applying to finite-time mean square asymptotic stability of the stochastic neural network, and the finite-time stability of stochastic chaotic neural networks in pth moment is less studied by the existing works.…”

Finite-time synchronization of uncertain complex dynamic networks with time-varying delay

“…In Ref. [17], the author investigated a class of finite-time boundedness synchronization of stochastic complex networks. In Ref.…”

“…Li et al [16] obtained several sufficient conditions for finite-time synchronization of nonlinearly coupled networks with time-varying delay by performing a new analysis. The finite-time non-fragile synchronization of stochastic complex networks was evaluated in [17]. Xiao and Gan [18] used a continuous finite-time controller and combined linear feedback with finite-time control theory to accomplish the finite-time synchronization of a complex dynamic network with delay.…”

H∞ Synchronization of Semi‐Markovian Jump Neural Networks with Randomly Occurring Time‐Varying Delays

“…It has tremendous application prospect, especially in robotics [1], pattern recognition [2,3], associative memory [4][5][6], identification [7,8], and combinatorial optimization [9][10][11][12]. Neural networks can be simply divided into the deterministic neural networks and stochastic neural networks based on whether they are disturbed by outside noise [13]. When the system is undisturbed, the deterministic neural network can describe the actual system accurately [13].…”

“…Neural networks can be simply divided into the deterministic neural networks and stochastic neural networks based on whether they are disturbed by outside noise [13]. When the system is undisturbed, the deterministic neural network can describe the actual system accurately [13]. Nevertheless, as far as we know, the actual system is generally uncertain and most of the physical system will be affected by random parameter variation and structure change [14][15][16].…”