We study control properties of a linearized fluid–structure interaction system, where the structure is a rigid body and where the fluid is a viscoelastic material. We establish the approximate controllability and the exponential stabilizability for the velocities of the fluid and of the rigid body and for the position of the rigid body. In order to prove this, we prove a general result for this kind of systems that generalizes in particular the case without structure. The exponential stabilization of the system is obtained with a finite-dimensional feedback control acting only on the momentum equation on a subset of the fluid domain and up to some rate that depends on the coefficients of the system. We also show that as in the case without structure, the system is not exactly null-controllable in finite time.

我们研究线性流固耦合系统的控制特性，其中结构是刚体，流体是粘弹性材料。我们建立了流体和刚体速度以及刚体位置的近似可控性和指数稳定性。为了证明这一点，我们证明了这种系统的一般结果，该结果特别概括了没有结构的情况。系统的指数稳定性是通过有限维反馈控制获得的，该控制仅作用于流体域子集上的动量方程，并达到取决于系统系数的某个速率。我们还表明，在没有结构的情况下，系统在有限时间内不是完全零可控的。