Boundary Mittag-Leffler stabilization of coupled time fractional order reaction-advection-diffusion systems with non-constant coefficients. (English) Zbl 1478.93499
Summary: 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.
MSC:
| 93D15 | Stabilization of systems by feedback |
| 93C20 | Control/observation systems governed by partial differential equations |
| 35K57 | Reaction-diffusion equations |
| 35R11 | Fractional partial differential equations |
Keywords:
boundary Mittag-Leffler stabilization; coupled time fractional order reaction-advection-diffusion systems; backstepping; non-constant coefficientsReferences:
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