Stabilization of bilinear systems with distributed delays using the Banach state space decomposition method

The strong stabilization of the considered system is established by presenting sufficient conditions based on an observability condition expressed by the semigroup solution of the linear part of the bilinear system. An explicit estimate on the convergence of the decay rate is established. Moreover, some sufficient conditions are used to discuss the weak stabilization of the considered system. Additionally, an illustrative example with numerical simulations is included.