TY - GEN
T1 - Local exponential stabilization of nonlinear infinite-dimensional systems
AU - HASTIR, Anthony
AU - WINKIN, Joseph
AU - Dochain, Denis
N1 - Funding Information:
VII. ACKNOWLEDGMENTS This research was conducted with the financial support of F.R.S-FNRS. Anthony Hastir is a FNRS Research Fellow under the grant FC 29535. The scientific responsibility rests with its authors.
Publisher Copyright:
© 2021 IEEE.
PY - 2021
Y1 - 2021
N2 - Local exponential stabilization of nonlinear distributed parameter systems (DPS) by linear state feedbacks is adressed. The results rely on an adapted concept of Fréchet differentiability which is in general easier to deal with. As main contribution, it is first shown how to link the Fréchet differentiability of the nonlinear semigroup generated by the operator dynamics with the Fréchet differentiability of the closed-loop semigroup obtained by injecting a linear state feedback into the dynamics. As a second result, an appropriately stabilizing state feedback for the linearized system around any equilibrium is proved to be locally stabilizing for the nonlinear system, under some boundedness assumption on the control operator. A class of controlled systems satisfying the required assumptions is then identified. The theoretical results are illustrated for the state regulation of a diffusion equation perturbed by a nonlinear term.
AB - Local exponential stabilization of nonlinear distributed parameter systems (DPS) by linear state feedbacks is adressed. The results rely on an adapted concept of Fréchet differentiability which is in general easier to deal with. As main contribution, it is first shown how to link the Fréchet differentiability of the nonlinear semigroup generated by the operator dynamics with the Fréchet differentiability of the closed-loop semigroup obtained by injecting a linear state feedback into the dynamics. As a second result, an appropriately stabilizing state feedback for the linearized system around any equilibrium is proved to be locally stabilizing for the nonlinear system, under some boundedness assumption on the control operator. A class of controlled systems satisfying the required assumptions is then identified. The theoretical results are illustrated for the state regulation of a diffusion equation perturbed by a nonlinear term.
UR - http://www.scopus.com/inward/record.url?scp=85125997928&partnerID=8YFLogxK
U2 - 10.1109/cdc45484.2021.9683165
DO - 10.1109/cdc45484.2021.9683165
M3 - Conference contribution
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 4038
EP - 4045
BT - 60th IEEE Conference on Decision and Control, CDC 2021
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 60th Conference on Decision and Control (CDC)
Y2 - 13 December 2021 through 17 December 2021
ER -