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This paper deals with bilinear systems evolving in a Banach state space (which is not necessarily reflexive). To the best of our knowledge, strong and weak-star stabilisation of control systems in nonreflexive state spaces has not been studied yet. This work is a first attempt towards providing sufficient conditions that guarantee the weak-star stabilisation of the system at hand. The strong stabilisation is stated as well. The approach uses results relying on convex analysis and some properties of the duality mapping and linear semigroup theory. Applications to reaction–diffusion and transport equations are further presented.

Strong and weak-star stabilisation of bilinear systems on nonreflexive Banach spaces