Feedback stabilization of non‐homogeneous bilinear systems with a finite time delay

Abstract

This paper investigates the feedback stabilization of non‐homogeneous delayed bilinear systems in Hilbert state space. More precisely, under an observability‐like assumption, we prove the exponential and strong stability of the solution by using bounded feedback control. Partial stabilization is discussed as well. The proofs of the main results are based on the decomposition method. The decay estimates of the stabilized solutions are obtained. Finally, some examples are presented.