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.
Regional Stabilization of the 1-D Kuramoto-Sivashinsky Equation via Modal Decomposition / Katz, Rami; Fridman, E.. - In: IEEE CONTROL SYSTEMS LETTERS. - ISSN 2475-1456. - 6:(2022), pp. 1814-1819. [10.1109/LCSYS.2021.3133492]
Regional Stabilization of the 1-D Kuramoto-Sivashinsky Equation via Modal Decomposition
Katz, Rami;
2022-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
