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Journal of Control Science and Engineering
Volume 2015, Article ID 164274, 10 pages
Research Article

Anticollocated Backstepping Observer Design for a Class of Coupled Reaction-Diffusion PDEs

Department of Electrical and Electronic Engineering, University of Cagliari, 09123 Cagliari, Italy

Received 10 September 2015; Accepted 4 November 2015

Academic Editor: Ai-Guo Wu

Copyright © 2015 Antonello Baccoli and Alessandro Pisano. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The state observation problem is tackled for a system of coupled reaction-diffusion PDEs, possessing the same diffusivity parameter and equipped with boundary sensing devices. Particularly, a backstepping-based observer is designed and the exponential stability of the error system is proven with an arbitrarily fast convergence rate. The transformation kernel matrix is derived in the explicit form by using the method of successive approximations, thereby yielding the observer gains in the explicit form, too. Simulation results support the effectiveness of the suggested design.