Lyapunov Functionals for Output Regulation of Exponentially Stable Semigroups via Integral Action and Application to Hyperbolic Systems

The paper deals with output feedback stabilization of exponentially stable systems by integral controllers. We propose appropriate Lyapunov functionals to prove exponential stability of the closed-loop systems. An example of parabolic PDE (partial differential equation) systems and an example of hyperbolic systems are worked out to show how exponentially stabilizing integral controllers are designed. The contribution of the paper is extending the forwarding technique to infinite-dimensional systems by elaborating Lyapunov functionals.