High-gain Observer-based Output Feedback Control with Sensor Dynamic Governed by Parabolic PDE

Abstract In this paper it is proposed to extend the result described in Khalil and Praly (2014) and the references therein, regarding the high-gain observer-based nonlinear control to the case of systems with diffusion sensor dynamic. Based on some usual hypotheses, we provide sufficient conditions involving the high-gain parameter and the length on the PDE sensor. In fact it is brought into light an explicit trade off between them: the larger the observer gain, the smaller the length of the PDE sensor needs to be. The stability analysis of the closed loop is based on a Lyapunov functional.