Observer design for a class of wave equation driven by an unknown periodic input

In this paper, exponentially convergent observers are designed for a class of wave equation driven by an unknown periodic input with only boundary sensing available. The problem is posed as a problem of designing an invertible coordinate transformation of the observer error system into an exponentially stable system. Observer gains (output injection function) are shown to satisfy a well-posed wave equation. Moreover, the observer gains are obtained in closed form.