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This paper investigates global strong stabilization of time-delayed bilinear systems on a real Hilbert state space. Sufficient conditions for strong global stabilization are formulated in terms of observability like assumptions. An explicit decay rate of the stabilized state is provided. Illustrative examples are presented.

In this paper, we discuss the problem of feedback stabilization for distributed bilinear systems with discrete delay evolving on a Hilbert state space. Firstly, we prove the existence and uniqueness of the mild solution of system at hand. Secondly, we study the weak and strong stabilization. More precisely, we provide some sufficient conditions to ensure the weak and strong stabilization for the delayed bilinear system. Moreover, in the case of the strong stabilization, an explicit decay estimate is established. Applications to wave and heat equations with delayed bilinear parts are considered.

In this work, we study in a Hilbert state space, the partial stabilisation of non-homogeneous bilinear systems using a bounded control. Necessary and sufficient conditions for weak and strong stabilisation are formulated in term of approximate observability like assumptions. Applications to parabolic and hyperbolic equations are presented.