Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8947615 | European Journal of Control | 2018 | 19 Pages |
Abstract
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 1âd 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.
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Physical Sciences and Engineering
Engineering
Control and Systems Engineering
Authors
Habib Ayadi,