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For bilinear infinite-dimensional dynamical systems, we show the equivalencebetween uniform global asymptotic stability and integral input-to-statestability. We provide two proofs of this fact. One applies to general systemsover Banach spaces. The other is restricted to Hilbert spaces, but is moreconstructive and results in an explicit form of iISS Lyapunov functions.

Characterizations of integral input-to-state stability for bilinear systems in infinite dimensions