Feedback logarithmic stabilisation of retarded bilinear systems of neutral type

In this paper, we deal with the problem of stabilisation for a class of retarded distributed bilinear systems of neutral type evolving in a Hilbert space. We first give a proof for the existence and uniqueness of the solution for the considered systems. Then, under a null controllability condition, we establish the stabilisation result and provide an explicit estimate of the energy decay. We also, examine the particular case where the semigroup associated with the linear part of the system is differentiable. Some illustrating applications to hyperbolic and parabolic equations are displayed.