Backstepping-based observer for output feedback stabilization of a boundary controlled fractional reaction diffusion system

Abstract

This paper is concerned with observer-based output feedback boundary control for a fractional reaction diffusion (FRD) system. The considered FRD system is endowed with only boundary sensing available and boundary actuation. First, to design a backstepping-based observer for the FRD system. Second, to combine a separately backstepping-based feedback controller and the proposed observer to generate an output feedback controller for stabilizing the FRD system. Third, to analyze the Mittag-Leffler stability of the observer error system and the controlled FRD system. Finally, to verify the validness of our proposed method for the controlled FRD system and the observer error system through a numerical example.