Input-Output Stability of a Reaction Diffusion Equation with In-domain Disturbances

The input-output stability (IOS) of a reaction-diffusion equation by means of a finite-dimensional linear time-invariant control system is studied. The reaction-diffusion plant admits a finite number of unstable poles and is open-loop unstable. The infinite-dimensional plant is put in feedback with a dynamic controller to achieve output stability via a Dirichlet boundary measurement and regulated output. The control design problem consists of deriving sufficient conditions in the form of matrix inequalities which allows us to show that the order of the finite-dimensional controller can be selected large enough to achieve IOS even when the control design is not optimal.