Finite Dimensional Compensators for Parabolic Distributed Systems with Unbounded Control and Observation

1984 ◽  
Vol 22 (2) ◽  
pp. 255-276 ◽  
Author(s):  
Ruth F. Curtain
Keyword(s):  
Distributed Systems ◽  
Unbounded Control ◽  
Finite Dimensional

Wavelet-like collocation method for finite-dimensional reduction of distributed systems

2000 ◽  
Vol 24 (12) ◽  
pp. 2687-2703 ◽  
Author(s):  
A. Adrover ◽  
G. Continillo ◽  
S. Crescitelli ◽  
M. Giona ◽  
L. Russo
Keyword(s):  
Distributed Systems ◽  
Collocation Method ◽  
Dimensional Reduction ◽  
Finite Dimensional Reduction ◽  
Finite Dimensional

Local feedback stabilization of time-periodic evolution equations by finite dimensional controls

2020 ◽  
Vol 26 ◽  
pp. 101
Author(s):  
Mehdi Badra ◽  
Debanjana Mitra ◽  
Mythily Ramaswamy ◽  
Jean-Pierre Raymond
Keyword(s):  
Periodic Solutions ◽  
Evolution Equations ◽  
Stokes Equations ◽  
Finite Dimension ◽  
Parabolic Systems ◽  
Feedback Stabilization ◽  
Navier Stokes ◽  
Dimensional System ◽  
Unbounded Control ◽  
Finite Dimensional

We study the feedback stabilization around periodic solutions of parabolic control systems with unbounded control operators, by controls of finite dimension. We prove that the stabilization of the infinite dimensional system relies on the stabilization of a finite dimensional control system obtained by projection and next transformed via its Floquet-Lyapunov representation. We emphasize that this approach allows us to define feedback control laws by solving Riccati equations of finite dimension. This approach, which has been developed in the recent years for the boundary stabilization of autonomous parabolic systems, seems to be totally new for the stabilization of periodic systems of infinite dimension. We apply results obtained for the linearized system to prove a local stabilization result, around periodic solutions, of the Navier-Stokes equations, by finite dimensional Dirichlet boundary controls.

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