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Exponential \(H_{\infty }\) Synchronization of Lur’e Complex Dynamical Networks Using Pinning Sampled-Data Control

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Abstract

This study is concerned with the exponential \(H_{\infty }\) synchronization criteria for complex dynamical networks of Lur’e- type systems with non-delay and delay couplings as well as external disturbances. The pinning sampled-data control is designed to achieve synchronization, in which only the selection of nodes is controlled, instead of the whole network. By constructing an improved Lyapunov–Krasovskii functional and utilizing the reciprocal convex method, the sufficient conditions are expressed in terms of linear matrix inequalities to ensure synchronization of the proposed network with a guaranteed \(H_{\infty }\) performance. Different from most existing studies, the addressed synchronization criteria depend not only on the upper bounds of the sampling intervals but also on the lower bounds; therefore, potentially leading to reduced conservative criteria. The desired control gain matrices are calculated by solving the obtained linear matrix inequalities that guarantee the exponential stability of the error system under the \(H_{\infty }\) norm. Finally, the effectiveness of the proposed method is demonstrated through numerical simulations.

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Authors and Affiliations

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

    R. Rakkiyappan, V. Preethi Latha & K. Sivaranjani

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  1. R. Rakkiyappan
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  2. V. Preethi Latha
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  3. K. Sivaranjani
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Correspondence to R. Rakkiyappan.

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Rakkiyappan, R., Latha, V.P. & Sivaranjani, K. Exponential \(H_{\infty }\) Synchronization of Lur’e Complex Dynamical Networks Using Pinning Sampled-Data Control. Circuits Syst Signal Process 36, 3958–3982 (2017). https://doi.org/10.1007/s00034-017-0508-7

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