Can one control the vibrations of a drum?
The problem of constructing feedback stabilizing controllers for the wave operator on \(\mathbb{R}^n\) (more generally AR systems determined by a hyperbolic operator) is under consideration. Toward this end, the notion of an input-output structure of a distributed system is clarified. A structure which generalizes the standard causal structure of lumped systems determined by the flow of time is used. On this base, feedback controllers that stabilize the wave equation along directions given by a proper cone in \(\mathbb{R}^n\) are constructed.
scientific article; zbMATH DE number 1488494
scientific article