On BIBO-stability of infinite-dimensional systems

We investigate the BIBO-stability (bounded-input-bounded-output stability) of infinite-dimensional dynamical systems represented in state space form. There the challenge lies within the intricate interplay between the L∞-norms and the Hilbert space structure. Apart from studying sufficient conditions guaranteeing BIBO-stability in the special case of Riesz-spectral systems, we discuss to which extent this notion is preserved under additive and multiplicative perturbations of the system. We find that, while the latter do in general not preserve BIBO-stability, certain additive perturbations of systems with analytic semigroups do. This contribution is based upon joint work with Felix L. Schwenninger and Hans Zwart.