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Dynamics and control of the active control system with the state-dependent actuation time delay

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Abstract

In this paper, a model of active control system with state-dependent actuation time delay is investigated. Galerkin projection scheme is used to obtain its low dimensional approximation system. State-dependency and effect on dynamics and performance of actuation delay in this active control system are considered. The following results are obtained. Firstly, a state-dependent actuation delay is proposed, which has never been reported in the previous works. It displays that actuation delay is state-dependent. Secondly, employing Galerkin projection scheme, low dimensional approximation system of this delayed active control system is obtained. At last, its stability and Hopf bifurcation are investigated by Routh-Hurwitz Criterion and Hopf bifurcation theory. Using software WinPP, numerical simulation is executed and supports the theoretical results in this paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, P.R. China

    Lijun Pei & Huifang Jia

  2. Basic Teaching Department, Zhengzhou University of Industry Technology, Zhengzhou, Henan 451100, P.R. China

    Huifang Jia

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  1. Lijun Pei
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  2. Huifang Jia
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Correspondence to Lijun Pei.

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Pei, L., Jia, H. Dynamics and control of the active control system with the state-dependent actuation time delay. Eur. Phys. J. Spec. Top. 229, 2275–2293 (2020). https://doi.org/10.1140/epjst/e2020-900148-9

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