Abstract
This paper deals with the problem of feedback stabilisation of bilinear systems with discrete delay in a Hilbert space. We consider the decomposition of the phase space and we propose a bounded feedback control to study the weak, strong and exponential stabilisation. Firstly, we discuss the well possedness of mild solutions of the considered systems. Secondly, some sufficient conditions are given to guarantee the feedback stabilisation for the bilinear systems. The stabilisation results are given in term of observation estimates. Furthermore, an explicit decay estimate of the stabilised state is obtained in the strong stabilisation case. At the end, examples with numerical simulations are given to show the applicability of our theoretical results.
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