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Stochastic Sampled-Data Control for Exponential Synchronization of Markovian Jumping Complex Dynamical Networks with Mode-Dependent Time-Varying Coupling Delay

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Abstract

In this paper, we address the problem of exponential synchronization of Markovian jumping complex dynamical networks with mode-dependent time-varying coupling delay via a stochastic sampled-data controller. In addition, the sampling period is assumed to be time-varying and switches between \(m\) different values in a random way with given probability. By constructing a new Lyapunov–Krasovskii functional (LKF) with triple integral terms and by employing convex combination technique and free weighting matrices method, sufficient conditions for the coupled complex dynamical network to be globally exponentially synchronized in the mean square sense are derived. The information about the lower bound of the discrete time-varying delay is used in the LKF. Based on the derived condition, the desired sampled-data feedback controller is designed in terms of the solution to linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.

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Acknowledgments

This work was supported by the NBHM Research Project (Grant Nos. 2/48(7)/2012/NBHM(R.P.)/R and D II/12669).

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  1. Department of Mathematics, Bharathiar University, Coimbatore , 641 046, Tamilnadu, India

    R. Rakkiyappan & N. Sakthivel

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  1. R. Rakkiyappan
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  2. N. Sakthivel
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Correspondence to R. Rakkiyappan.

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Rakkiyappan, R., Sakthivel, N. Stochastic Sampled-Data Control for Exponential Synchronization of Markovian Jumping Complex Dynamical Networks with Mode-Dependent Time-Varying Coupling Delay. Circuits Syst Signal Process 34, 153–183 (2015). https://doi.org/10.1007/s00034-014-9854-x

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