论文标题
反馈稳定输入延迟的抛物线系统
Feedback stabilization of parabolic systems with input delay
论文作者
论文摘要
这项工作致力于具有有限维控制的抛物线系统的稳定。我们的主要结果表明，Fattorini-Hautus标准产生了这种反馈控制的存在，例如在稳定的情况下毫不延迟。该证明是将系统拆分为有限的尺寸不稳定部分和稳定的无限尺寸部分，并将Artstein变换应用于有限维系统上以消除控件的延迟。使用我们的抽象结果，我们可以证明具有持续延迟的抛物线系统稳定的新结果：$ n $维线性对流扩散方程，具有$ n \ geq 1 $和OSEEN系统。我们通过表明该理论可以用来通过证明固定状态周围Navier-Stokes系统的局部反馈分布式稳定来结束文章，以表明该理论可用于稳定非线性抛物线系统。
This work is devoted to the stabilization of parabolic systems with a finite-dimensional control subjected to a constant delay. Our main result shows that the Fattorini-Hautus criterion yields the existence of such a feedback control, as in the case of stabilization without delay. The proof consists in splitting the system into a finite dimensional unstable part and a stable infinite-dimensional part and to apply the Artstein transformation on the finite-dimensional system to remove the delay in the control. Using our abstract result, we can prove new results for the stabilization of parabolic systems with constant delay: the $N$-dimensional linear convection-diffusion equation with $N\geq 1$ and the Oseen system. We end the article by showing that this theory can be used to stabilize nonlinear parabolic systems with input delay by proving the local feedback distributed stabilization of the Navier-Stokes system around a stationary state.
