Exponential synchronization of Markovian jumping complex dynamical networks with randomly occurring parameter uncertainties

2014 ◽  
Vol 78 (1) ◽  
pp. 15-27 ◽  
Author(s):  
Wuneng Zhou ◽  
Anding Dai ◽  
Jun Yang ◽  
Huashan Liu ◽  
Xueliang Liu
Keyword(s):  
Exponential Synchronization ◽  
Complex Dynamical Networks ◽  
Parameter Uncertainties ◽  
Markovian Jumping ◽  
Dynamical Networks

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

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.

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

2013 ◽  
Vol 2013 ◽  
pp. 1-21 ◽  
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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