Observer Design for Boundary Coupled Fractional Order Distributed Parameter Systems

Abstract

This paper studies the observer design for the fractional order boundary coupled distributed parameter systems. Firstly, we obtain the decoupled observer error systems from the state system and observer system. Secondly, the advection terms are eliminated through the invertible transformation and we can obtain the general reaction-diffusion partial differential equations, which are more convenient for discussions. Thirdly, Backstepping method and target systems are employed to give kernel partial differential equations and then the related observer gains can be derived from the corresponding kernels. Finally, Mittag-Leffler stability of the designed fractional order observers is analyzed and the main results are illustrated by the simulation graphically.