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Volume 6 Issue 4
Jul.  2019

IEEE/CAA Journal of Automatica Sinica

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Aye Aye Than and Junmin Wang, "Stabilization of the Cascaded ODE-Schrödinger Equations Subject to Observation With Time Delay," IEEE/CAA J. Autom. Sinica, vol. 6, no. 4, pp. 1027-1035, June 2019. doi: 10.1109/JAS.2019.1911588
Citation: Aye Aye Than and Junmin Wang, "Stabilization of the Cascaded ODE-Schrödinger Equations Subject to Observation With Time Delay," IEEE/CAA J. Autom. Sinica, vol. 6, no. 4, pp. 1027-1035, June 2019. doi: 10.1109/JAS.2019.1911588

Stabilization of the Cascaded ODE-Schrödinger Equations Subject to Observation With Time Delay

doi: 10.1109/JAS.2019.1911588
Funds:  Manuscript received September 9, 2018; revised October 12, 2018; accepted November 8, 2018. This work was supported by the National Natural Science Foundation of China (61673061)
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  • This paper focuses on the stabilization of the cascaded Schrödinger-ODE equations subject to the observation with time delay. Both observer and predictor systems are designed to estimate the state variable on the time interval $[0, t-\tau]$ when the observation is available, and to predict the state variable on the time interval $[t-\tau, t]$ when the observation is not available, respectively. Based on the estimated state variable and the output feedback stabilizing controller using the backstepping method, it is shown that the closed-loop system is exponentially stable.

     

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    Highlights

    • We present a unified method to compensate the Schrödinger equation cascaded by the ODE equations, where the observation of the system has the time delay.
    • We prove the well-posedness of the open-loop system in the sense of the Salamon-Weiss well-posed infinite dimensional system theory.
    • We design the observer and predictor systems, respectively, at the time interval when the observation is available, and when the observation is not available, so that we can construct a control law with the estimated state by the observer and predictor to stabilize the cascaded PDE-ODE system.
    • We prove the closed-loop system is exponentially stable for the smooth initial values.

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