Finite-time synchronisation control of coupled reaction-diffusion systems

Xin-Xin Han, Hai-Yan Yu and Kai-Ning Wu

International Journal of Systems Science, 2019, vol. 50, issue 15, 2838-2852

Abstract: We consider the finite-time synchronisation for coupled reaction-diffusion systems. At first, we design a pinning control strategy for the coupled systems. For the uncontrolled nodes, we use the adaptive adjustment to the coupling strength. Based on the Poincaré inequality technique and using the finite-time stability lemma, we obtain the sufficient condition to ensure the finite-time synchronisation. Time delay occurs usually in the coupled systems and when there exist time-varying delays in the coupled reaction-diffusion systems, we design a controller to impel the coupled systems to achieve the finite-time synchronisation. Finally, numerical examples are given to illustrate our theoretical results.

Date: 2019
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DOI: 10.1080/00207721.2019.1690718

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