Stabilization of an ODEaSchroedinger Cascade

We consider the problem of stabilization of a linear ODE with input dynamics governed by the linearized Schroedinger equation. The interconnection between the ODE and Schroedinger equation is bi-directional at a single point. We construct an explicit feedback law that compensates the Schroedinger dy...

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Bibliographic Details
Published inSystems & control letters Vol. 62; no. 6; pp. 503 - 510
Main Authors Ren, Beibei, Wang, Jun-Min, Krstic, Miroslav
Format Journal Article
LanguageEnglish
Published 01.06.2013
Subjects
Control systems
Decay rate
Design engineering
Dynamical systems
Dynamics
Schroedinger equation
Stabilization
Transformations
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Summary:We consider the problem of stabilization of a linear ODE with input dynamics governed by the linearized Schroedinger equation. The interconnection between the ODE and Schroedinger equation is bi-directional at a single point. We construct an explicit feedback law that compensates the Schroedinger dynamics at the inputs of the ODE and stabilizes the overall system. Our design is based on a two-step backstepping transformation by introducing an intermediate system and an intermediate control. By adopting the Riesz basis approach, the exponential stability of the closed-loop system is built with the pre-designed decay rate and the spectrum-determined growth condition is obtained. A numerical simulation is provided to illustrate the effectiveness of the proposed design.
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ISSN:0167-6911