Boundary feedback stabilization of a reaction–diffusion equation with Robin boundary conditions and state-delay. (June 2020)

• Record Type: Journal Article
• Authors: Lhachemi, Hugo; Shorten, Robert
• Is Part Of: Automatica. Volume 116(2020)
• Publication Date: 2020-06
• Subjects: Distributed parameter systems -- Boundary control -- State-delay -- Reaction–diffusion equation -- Input-to-state stability; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2020.108931
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper discusses the boundary feedback stabilization of a reaction–diffusion equation with Robin boundary conditions and in the presence of a time-varying state-delay. The proposed control design strategy is based on a finite-dimensional truncated model obtained via a spectral decomposition. By an adequate selection of the number of modes of the original infinite-dimensional system, we show that the design performed on the finite-dimensional truncated model achieves the exponential stabilization of the original infinite-dimensional system. In the presence of distributed disturbances, we show that the closed-loop system is exponentially input-to-state stable with fading memory.