Design of Infinite-Dimensional Observers for a Linearized Water Wave System With Distributed or Point Measurement

The article deals with synthesis of observers for a linearized water wave system (LWWS) confined in a bounded rectangular fluid domain. To estimate the state of LWWS, including velocity potential and wave elevation, infinite-dimensional state observers are designed by using two different observation measurements. The first observer is designed by measuring the distributed free-surface wave elevation. The convergence rate of this observer is proved to be exponential and fast. The second observer is designed by using only the surface measurement of wave elevation at a fixed point. We show that the second observer converges strongly and more slowly than the first one. The performances of the two designed observers are validated by our numerical simulations.