Strong and exponential stabilization of linear boundary control systems

Abstract

In this work, we focus on the problem of stabilizing boundary control systems. Studying such boundary control systems is widely recognized as a complex issue. To tackle this issue, we employ a strategy that involves transforming the stabilization problem into a corresponding linear internal control system. By utilizing this transformation, we simplify the analysis of boundary stabilization problems and make the most of the extensive body of existing literature. To achieve exponential stability, we utilize spectral decomposition. Additionally, we explore the strong stabilization of a broad class of Riesz-spectral boundary control problems. We apply our findings to a class of heat equations and provide numerical simulations to illustrate these results.