Feedback Stabilization of Delayed Bilinear Systems

Abstract

In this paper, we discuss the problem of feedback stabilization for distributed bilinear systems with discrete delay evolving on a Hilbert state space. Firstly, we prove the existence and uniqueness of the mild solution of system at hand. Secondly, we study the weak and strong stabilization. More precisely, we provide some sufficient conditions to ensure the weak and strong stabilization for the delayed bilinear system. Moreover, in the case of the strong stabilization, an explicit decay estimate is established. Applications to wave and heat equations with delayed bilinear parts are considered.