This paper is concerned with boundary control for a class of coupled time fractional order reaction–advection–diffusion (FRAD) systems with non-constant coefficients (space-dependent coefficients) by state feedback. Partial differential equation (PDE) backstepping makes available to stabilize coupled time FRAD systems modeled by fractional PDEs. With boundary controller design and discussion on well-posedness of control kernel equations, the Mittag-Leffler stability of the closed-loop system is analyzed theoretically by the fractional Lyapunov method. A numerical scheme is constructed for coupled FRAD system to simulate numerical examples when the kernel equations have not the explicit solution. Comments on robustness to perturbation parameters in system coefficients are finally stated.

本文涉及一类状态反馈为非恒定系数（与空间有关的系数）的耦合时间分数阶反应-对流-扩散（FRAD）系统的边界控制。偏微分方程（PDE）反演可用于稳定由分数PDE建模的耦合时间FRAD系统。通过边界控制器的设计和对控制核方程的适定性的讨论，通过分数Lyapunov方法从理论上分析了闭环系统的Mittag-Leffler稳定性。当核方程没有显式解时，为耦合FRAD系统构造一个数值方案，以模拟数值示例。最后说明了系统系数对摄动参数的鲁棒性。