Abstract
Abstract In this paper, we investigate the stabilization problem of a cascade of a fractional ordinary differential equation (FODE) and a fractional reaction–diffusion (FRD) equation where the interconnections are of Neumann type. We exploit the partial differential equation backstepping method for designing a controller, which guarantees the Mittag–Leffler stability of the FODE-FRD cascade. Moreover, we propose an observer that is Mittag–Leffler convergent. Also, we propose an output feedback boundary controller, and we prove that the closed-loop FODE-FRD system is Mittag–Leffler stable in the sense of the corresponding norm. Finally, numerical simulations are presented to verify the results.
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More From: IMA Journal of Mathematical Control and Information
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