Feedback exponential stabilisation for delayed bilinear systems

In this paper, we investigate exponential and weak stabilization for delayed bilinear distributed systems in a Hilbert space, using bounded feedback control. We show the existence and uniqueness of a global mild solution and we show that this solution is exponentially stabilized under a condition of observability inequality. Moreover, we give an explicit rate for the exponential stabilization. Next, we discuss weak stabilization under a weaker condition. Finally, we present some applications of the results found.