Observer‐based output feedback compensator design for linear parabolic PDEs with local piecewise control and pointwise observation in space

This study presents an observer-based output feedback compensator design for a linear parabolic partial differential equation (PDE), where a finite number of actuators and sensors are active over partial areas and at specified points in the spatial domain, respectively. In the proposed design method, a Luenberger-type PDE observer is first constructed by using the non-collocated pointwise observation to exponentially track the PDE state. Based...