Stabilization of coupled ODE-PDE system with intermediate point and spatially varying effects interconnection. (English) Zbl 1366.93541
Summary: In this paper, the stabilization analysis problem of a bi-directional coupled ODE-PDE system is proposed. The spatially varying coefficient and the intermediate point interaction between the subsystems makes the coupled system more representative. An invertible infinite-dimensional backstepping transformation is introducted to bring the original system into an exponentially stable target system. By employing the backstepping method, the kernel functions in the transformations are worked out under some assumptions of the spatially varying coefficient. Then, an explicit state-feedback law is designed and the exponential stability of the transformed closed-loop system has been also discussed. Finally, numerical simulation is provided to illustrate the effectiveness of the proposed design.
MSC:
| 93D15 | Stabilization of systems by feedback |
| 93D20 | Asymptotic stability in control theory |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93C20 | Control/observation systems governed by partial differential equations |
Keywords:
coupled ODE-PDE system; spatially varying coefficient; intermediate point; backstepping method; exponential stabilityReferences:
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