This paper studies the Mittag-Leffler stabilization for unstable infinite dimensional systems actuated by boundary controllers described by time fractional reaction diffusion equations. Via the Riesz basis method, the stable and the unstable part of the considered system are separated. The Kalman rank criterion, which is a classical linear algebra condition, guarantees the stabilizability of the unstable subsystem. Based on these, a controller governed by a finite dimensional system (so called the finite dimensional controller hereafter) is designed to achieve the Mittag-Leffler stability of the closed loop. From infinite to finite, this methodology is a substantial improvement for the existing control laws.

本文研究了由时间分数反应扩散方程描述的边界控制器驱动的不稳定无限维系统的 Mittag-Leffler 稳定性。通过 Riesz 基方法，将所考虑系统的稳定部分和不稳定部分分开。卡尔曼秩准则是一个经典的线性代数条件，保证了不稳定子系统的稳定性。基于这些，设计了一个由有限维系统控制的控制器（以下称为有限维控制器），以实现闭环的 Mittag-Leffler 稳定性。从无限到有限，这种方法论是对现有控制律的实质性改进。