Output feedback stabilization of linear PDEs with finite dimensional input-output maps and Kelvin-Voigt damping

In this paper, we consider systems of partial differential equations with a finite relative degree between the input and the output. In such systems, an output feedback controller can be constructed to regulate the output with the desired convergence properties. Although the zero dynamics are infinite dimensional, we show that the controller alters the boundary conditions in such a way that it leads to a predictable expansion in the stable operating envelope of the system. Moreover, the expansion of the stable envelope depends only on the boundary conditions and the structure of the PDE, and is independent of the system parameters. The methodology is extended to output tracking and time-varying forcing functions as well. The phenomenon investigated in the paper is quite unique to partial differential equations and without any parallel in systems of ODEs.