Regional Weak and Strong Stabilization of Time Delay Infinite Dimensional Bilinear Systems

Abstract

This chapter centers its attention on achieving regional stabilization for infinite-dimensional bilinear systems with time delay that evolves within the spatial domain Ω. The central objective is to investigate the asymptotic patterns of such systems within a designated subregion ω of Ω. Subsequently, we proceed to showcase the realization of regional weak stabilization through the application of conditions related to weak observability. Furthermore, the potential for regional strong stabilization is demonstrated, contingent on the fulfillment of exact observability conditions. To validate the precision of the theoretical outcomes, we incorporate illustrative examples and simulations.