Boundary Stabilization for a Heat-Kelvin-Voigt Unstable Interaction Model, with Control and Partial Observation Localized at the Interface Only

A prototype model for a Fluid–Structure interaction is considered. We aim to stabilize [enhance stability of] the model by having access only to a portion of the state. Toward this goal we shall construct a compensator-based Luenberger design, with the following two goals: (1) reconstruct the original system asymptotically by tracking partial information about the full state, (2) stabilize the original unstable system by feeding an admissible control based on a system which is obtained from the compensator. The ultimate result is boundary control/stabilization of partially observed and originally unstable fluid–structure interaction with restricted information on the current state and without any knowledge of the initial condition. This prevents applicability of known methods in either open-loop or closed loop stabilization/control.