Exponential stabilization of cascade ODE-linearized KdV system by boundary Dirichlet actuation
In this paper, we solve the problem of exponential stabilization for a class of cascade ODE-PDE systems governed by a linear ordinary differential equation and the 1−d linearized Korteweg–de Vries equation (KdV) posed on a bounded interval. The control for the whole system acts in the left boundary...
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| Veröffentlicht in: | European journal of control 2018-09, Vol.43, p.33-38 |
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| creator | Ayadi, Habib |
| description | In this paper, we solve the problem of exponential stabilization for a class of cascade ODE-PDE systems governed by a linear ordinary differential equation and the 1−d linearized Korteweg–de Vries equation (KdV) posed on a bounded interval. The control for the whole system acts in the left boundary with Dirichlet condition of the KdV equation whereas the KdV acts in the linear ODE by a Dirichlet connection. We use the so-called backstepping method in infinite dimension to convert system under consideration to an exponentially stable cascade ODE-PDE system. Then, we use the invertibility of such design to achieve the exponential stability for the original ODE-PDE cascade system by using Lyapunov analysis. |
| doi_str_mv | 10.1016/j.ejcon.2018.05.005 |
| format | Article |
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| identifier | ISSN: 0947-3580 |
| ispartof | European journal of control, 2018-09, Vol.43, p.33-38 |
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| language | eng |
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| source | ProQuest Central UK/Ireland; Alma/SFX Local Collection |
| subjects | Actuation Backstepping Boundary conditions Cascade ODE-PDE Controllers Dirichlet problem Exponential stability Hilbert space Korteweg-Devries equation Linearization Linearized-KdV Partial differential equations Stability analysis Water waves |
| title | Exponential stabilization of cascade ODE-linearized KdV system by boundary Dirichlet actuation |
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