Observer-based output feedback control design for a coupled system of fractional ordinary and reaction–diffusion equations
Keyword(s):
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.
2018 ◽
Vol 12
(11)
◽
pp. 1561-1572
◽
1995 ◽
Vol 46
(3)
◽
pp. 366-383
◽
2018 ◽
Vol 141
(2)
◽
Keyword(s):
2019 ◽
Vol 16
(3)
◽
pp. 1430
2018 ◽
Vol 27
(2)
◽
pp. 605-621
◽
2022 ◽
pp. 106232
2020 ◽
Vol 378
◽
pp. 112935
◽