Backstepping Design of Dynamic State Feedback Controllers for Parabolic Systems
arXiv:2609.17293
Abstract
Recently, dynamic state feedback controllers that are based on dynamic extensions have been presented for heterodirectional hyperbolic systems. In this paper, a similar concept for the control of coupled diffusion-reaction systems is suggested. The introduction of a specific controller dynamics leads to homogenized diffusion coefficients for the extended system. Then, a backstepping-based static state feedback for the dynamically extended system is designed, which, overall, results in a dynamic state feedback. Such a design allows stabilizing a more general class of parabolic systems as well as assigning arbitrary closed-loop dynamics. This can be used, e.g., to achieve a decoupled input-output behavior, which is, in general, not possible with a static state feedback. A simulation example illustrates the results.
accepted for 65th IEEE Conference on Decision and Control (CDC 2026)