Feedback stabilization of non-homogeneous semilinear neutral systems with distributed delay

Abstract This paper addresses the stabilization problem for a class of non-homogeneous semilinear neutral systems with distributed delay, evolving on a real Hilbert space. Sufficient conditions in terms of observation estimates are given to achieve the strong stabilization via bounded feedback control. Moreover, under an appropriate decomposition of the state space, we consider a feedback control that depends only on the state projection on a suitable subspace and guarantee the exponential stabilization in the bilinear case. Finally, we present examples and numerical simulations to illustrate the effectiveness of the obtained results.