Correction to “Output Feedback Stabilization of a One-Dimensional Schrödinger Equation by Boundary Observation with Time Delay” [May 10 1226-1232

Guo, Bao‐Zhu; Yang, Kun-Yi

doi:10.1109/tac.2010.2051070

Cited by 13 publications

(16 citation statements)

References 2 publications

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“…For example, in the article [26], the boundary stabilization of a Schrödinger equation with variable coefficient where the boundary observation suffers from a fixed time delay was studied. This is a generalization of the similar work for the Schrödinger equation in [18] by using the separation principle [17] for constant coefficients. The variable coefficients make the system too complicated to estimate the solution, which relies on the estimation of the eigenvalues and eigenfunctions by asymptotic analysis.…”

Section: Introductionmentioning

confidence: 90%

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On the stability of the Schrödinger equation with time delay

Agirseven

2018

Filomat

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Section: Introductionmentioning

confidence: 90%

“…Theory and applications of delay linear and nonlinear Schrödinger equations with the delay term is an operator of lower order with respect to the operator term were widely investigated (see, e.g., [13,17,18,[25][26][27], and the references given therein).…”

Section: Introductionmentioning

confidence: 99%

On the stability of the Schrödinger equation with time delay

Agirseven

2018

Filomat

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“…Recently, for the interconnected system, Liu [14] has considered a wave-heat cascade system and the performance output regulation problem is solved. In distributed parameter system, Guo and Yang [15], [16] have applied this approach in Euler-Bernoulli beam equation and Schrödinger equation with time delay boundary observation and obtain the stability results. In [17], for a string equation with time delays in output feedback loop, the stability result has been obtained by spectral analysis method.…”

Section: Introductionmentioning

confidence: 99%

Performance Output Tracking for a One-Dimensional Wave Equation With Input Delay

Liu

2019

IEEE Access

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This paper is concerned with the performance output regulation problem for a wave equation with input delay and unmatched disturbance. Firstly, in the case of time delay, the input delay term is translated into a first-order hyperbolic equation and we obtain a cascade system. By applying the method of auxiliary trajectory, the unmatched disturbance is compensated and eliminated. Then, we design a state feedback controller. Meanwhile, with the measured error signal, we construct an observer for the cascade system. Based on the observer, an error feedback controller is developed by replacing the states with their estimations. By using Lyapunov functional method, we also prove the regulation error goes to zero exponentially. Thus, the problem of output tracking is solved for the wave equation in despite of input delay and unmatched disturbance. Finally, the numerical simulations are presented to validate the theoretical results. INDEX TERMS Wave equation, output regulation, time delay, unmatched disturbance.

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“…Recently, we solve stabilization of such distributed parameter systems in Guo et al as a 1‐dimensional wave, an Euler‐Bernoulli beam, and a Schrödinger equation with constant coefficients where observation or control is suffered from a given time delay. Comparing with the huge works on stabilization of constant coefficients equations with collocated observation, the study for non‐collocated PDEs control system with variable coefficient where observation suffered from time delay is still fairly scarce.…”

Section: Introductionmentioning

confidence: 99%

Stabilization of a one‐dimensional wave equation with variable coefficient under non‐collocated control and delayed observation

Yang

2017

Math Methods in App Sciences

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In this paper, we consider stabilization of a 1-dimensional wave equation with variable coefficient where non-collocated boundary observation suffers from an arbitrary time delay. Since input and output are non-collocated with each other, it is more complex to design the observer system. After showing well-posedness of the open-loop system, the observer and predictor systems are constructed to give the estimated state feedback controller. Different from the partial differential equation with constant coefficients, the variable coefficient causes mathematical difficulties of the stabilization problem. By the approach of Riesz basis property, it is shown that the closed-loop system is stable exponentially.Numerical simulations demonstrate the effect of the stable controller. This paper is devoted to the wave equation with variable coefficients generalized of that with constant coefficients for delayed observation and non-collocated control.

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Correction to “Output Feedback Stabilization of a One-Dimensional Schrödinger Equation by Boundary Observation with Time Delay” [May 10 1226-1232

Cited by 13 publications

References 2 publications

On the stability of the Schrödinger equation with time delay

On the stability of the Schrödinger equation with time delay

Performance Output Tracking for a One-Dimensional Wave Equation With Input Delay

Stabilization of a one‐dimensional wave equation with variable coefficient under non‐collocated control and delayed observation

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