TY - JOUR
T1 - Regional Stabilization of the 1-D Kuramoto-Sivashinsky Equation via Modal Decomposition
AU - Katz, Rami
AU - Fridman, Emilia
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2022
Y1 - 2022
N2 - In this letter, we suggest regional stabilization of the semilinear 1D KSE under nonlocal or boundary actuation. We employ modal decomposition and derive regional H^{1} stability conditions for the closed-loop system. Given a decay rate that defines the number of state modes in the controller, we provide LMIs for finding the the controller gain as well as a bound on the domain of attraction. In the case of boundary control, we suggest a dynamic extension with a novel internally stable dynamics. The latter allows to enlarge a bound on the domain of attraction. Numerical examples illustrate the efficiency of the method.
AB - In this letter, we suggest regional stabilization of the semilinear 1D KSE under nonlocal or boundary actuation. We employ modal decomposition and derive regional H^{1} stability conditions for the closed-loop system. Given a decay rate that defines the number of state modes in the controller, we provide LMIs for finding the the controller gain as well as a bound on the domain of attraction. In the case of boundary control, we suggest a dynamic extension with a novel internally stable dynamics. The latter allows to enlarge a bound on the domain of attraction. Numerical examples illustrate the efficiency of the method.
KW - Distributed parameter systems
KW - boundary control
KW - nonlinear parabolic PDEs
UR - http://www.scopus.com/inward/record.url?scp=85121368813&partnerID=8YFLogxK
U2 - 10.1109/LCSYS.2021.3133492
DO - 10.1109/LCSYS.2021.3133492
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AN - SCOPUS:85121368813
SN - 2475-1456
VL - 6
SP - 1814
EP - 1819
JO - IEEE Control Systems Letters
JF - IEEE Control Systems Letters
ER -