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Backstepping design for a class of coupled parabolic PDEs with spatially varying coefficient
Author(s) -
Ghaderi Najmeh,
Keyanpour Mohammad
Publication year - 2020
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.2104
Subject(s) - backstepping , control theory (sociology) , parabolic partial differential equation , controller (irrigation) , partial differential equation , mathematics , class (philosophy) , exponential function , state space , full state feedback , computer science , mathematical analysis , control (management) , adaptive control , artificial intelligence , statistics , agronomy , biology
In this paper, we concentrate on the state feedback stabilization of a class of coupled parabolic partial differential equations with space dependent diffusion coefficients. To stabilize the system, we design a state feedback controller using the backstepping technique. Namely, we convert the original system into a stable desired system called the target system to obtain a backstepping feedback controller. We prove that the feedback controller causes the main system to be exponential stable. Also, the numerical simulations show that validity and efficiency of theoretical results.