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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Synchronization of T-S Fuzzy Sampled-data Controller for H-R Neuron Model With Delay using a New Looped-Functional

Discontinuity, Nonlinearity, and Complexity 10(2) (2021) 259--273 | DOI:10.5890/DNC.2021.06.007

P. Nirvin$^1$ , R. Rakkiyappan$^1$

Department of Mathematics, Bharathiar University, Coimbatore - 641 046, Tamilnadu, India

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Abstract

This paper investigates the synchronization of Takagi-Sugeno (T-S) fuzzy sampled-data-controller for Hindmarsh-Rose (H-R) neuron model with constant {communication time delay} in the from the master-slave framework. The utilization of the state information of $e(t_k),~e(t),~e(t_{k+1}),~e(t_k-\lambda),~e(t-\lambda),~e(t_{k+1}-\lambda)$, is done adequately {be} the information of a novel looped-functional in the construction of a Lyapunov functional (LF). To establish that the slave system is synchronized with the master system, some satisfactory conditions with less conservativeness are derived by using the above mentioned functional and utilizing wirtingers inequality, jensen's inequalities, free matrix-based integral inequality method. The linear matrix inequality (LMI) techniques the fuzzy sampled-data control can be designed. Finally, a numerical example is given to illustrate the effectiveness of our theoretical results.

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