Stabilisation in distribution by delay feedback controls for hybrid stochastic delay differential equations

Li, Yuyuan and You, Surong and Lu, Jianqiu and Jiang, Yanan and Hu, Liangjian and Mao, Xuerong (2023) Stabilisation in distribution by delay feedback controls for hybrid stochastic delay differential equations. International Journal of Systems Science, 54 (5). pp. 1070-1086. ISSN 0020-7721 (https://doi.org/10.1080/00207721.2022.2160675)

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Abstract

This article aims to design a linear delay feedback control to stabilise an unstable hybrid stochastic delay differential equation in distribution. Under the global Lipschitz condition, sufficient criteria are established to guarantee the stability of the controlled system. Then LMI techniques are employed to design the control law in two structure forms: state feedback and output injection.