Exponential synchronization of Markovian jump complex dynamical networks with partially uncertain transition rates and stochastic disturbances

The exponential synchronization of a Markovian jump complex dynamical network with piecewise-constant transition rates is investigated. Two distinct types of time-varying delay are considered for the system; one is distributed time-delay for each node, the other is discrete coupling time-delay. Based on an augmented Lyapunov–Krasovskii functional, some sufficient conditions are derived and expressed in the form of linear matrix inequalities, which are formulated in such a manner as to determine the controller gain matrices. Finally, an example is given to illustrate the effectiveness and validity of the proposed method.

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Exponential Synchronization of Stochastic Complex Dynamical Networks with Impulsive Perturbations and Markovian Switching

Mathematical Problems in Engineering ◽

10.1155/2014/927858 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10

Author(s):

Wuneng Zhou ◽

Anding Dai ◽

Dongbing Tong ◽

Jun Yang

Keyword(s):

Stochastic Analysis ◽

Function Method ◽

Transition Probability ◽

Sufficient Conditions ◽

Exponential Synchronization ◽

Markovian Switching ◽

Complex Dynamical Networks ◽

Dynamical Networks ◽

Synchronization Problem ◽

Lyapunov Function Method

This paper investigates the exponential synchronization problem of stochastic complex dynamical networks with impulsive perturbation and Markovian switching. The complex dynamical networks consist ofκmodes, and the networks switch from one mode to another according to a Markovian chain with known transition probability. Based on the Lyapunov function method and stochastic analysis, by employingM-matrix approach, some sufficient conditions are presented to ensure the exponential synchronization of stochastic complex dynamical networks with impulsive perturbation and Markovian switching, and the upper bound of impulsive gain is evaluated. At the end of this paper, two numerical examples are included to show the effectiveness of our results.

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Exponential Synchronization for Neutral Complex Dynamical Networks with Interval Mode-Dependent Delays and Sampled Data

Mathematical Problems in Engineering ◽

10.1155/2013/639580 ◽

2013 ◽

Vol 2013 ◽

pp. 1-21 ◽

Cited By ~ 2

Author(s):

Xinghua Liu ◽

Hongsheng Xi

Keyword(s):

Exponential Stability ◽

Exponential Synchronization ◽

Complex Dynamical Networks ◽

Linear Matrix ◽

Stability Conditions ◽

Time Varying ◽

Sampled Data ◽

Neutral Complex ◽

Dynamical Networks ◽

Markovian Jump Parameters

The exponential synchronization and sampled-data controller problem for a class of neutral complex dynamical networks (NCDNs) with Markovian jump parameters, partially unknown transition rates and delays, is investigated in this paper. Both the discrete and neutral delays are considered to be interval mode dependent and time varying, while the sampling period is assumed to be time varying and bounded. Based on a new augmented stochastic Lyapunov functional, the delay-range-dependent and rate-dependent exponential stability conditions for the closed-loop error system are obtained by the Lyapunov-Krasovskii stability theory and reciprocally convex lemma. Then according to the proposed exponential stability conditions, the sampled-data synchronization controllers are designed in terms of the solution to linear matrix inequalities that can be solved effectively by using Matlab. Finally, numerical examples are given to demonstrate the feasibility and effectiveness of the proposed methods.

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Mean-Square Exponential Synchronization of Stochastic Complex Dynamical Networks with Switching Topology by Impulsive Control

Discrete Dynamics in Nature and Society ◽

10.1155/2013/932058 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8

Author(s):

Xuefei Wu ◽

Chen Xu

Keyword(s):

Impulsive Control ◽

Sufficient Conditions ◽

Exponential Synchronization ◽

Complex Dynamical Networks ◽

Switching Topology ◽

Linear Matrix ◽

Mean Square ◽

Dynamical Networks ◽

The Mean ◽

Networks With Switching Topology

This paper investigates the mean-square exponential synchronization issues of delayed stochastic complex dynamical networks with switching topology and impulsive control. By using the Lyapunov functional method, impulsive control theory, and linear matrix inequality (LMI) approaches, some sufficient conditions are derived to guarantee the mean-square exponential synchronization of delay complex dynamical network with switch topology, which are independent of the network size and switch topology. Numerical simulations are given to illustrate the effectiveness of the obtained results in the end.

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