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In this paper we deal with the problem of strong stabilisation for a class of distributed semilinear systems by means of a nonlinear feedback control. The systems under consideration evolve in a Hilbert space and present periodic time-varying state delay. 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 optimal decay rate estimate. The particular case of such systems for which the linear part generates a differentiable semigroup is also investigated. Some illustrating applications to hyperbolic and parabolic equations are displayed. Finally, a conclusion and some perspectives are given. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the problem of stabilisation for a class of distributed semilinear systems. The considered systems present a state time delay and evolve in Banach spaces. A new stabilising feedback control is proposed. Two kinds of stabilizability, namely exponential and weak stabilizability, are investigated. An explicit estimate of the energy decay rate is given. Some illustrating applications to parabolic and hyperbolic equations with numerical simulations are considered. [ABSTRACT FROM AUTHOR]