Various results concerning set input-to-state stability

Regarding the input-to-state stability (ISS) property, we extend it to arbitrary closed invariant sets various results which were previously known for the case of equilibria. In particular, we show the equivalence between stabilizability and feedback equivalence to ISS systems. In addition for the compact attractor case, we provide Lyapunov and dissipation-theoretic characterizations, and we relate this case to the notion of "practical" ISS (ISpS), a notion which appears in the context of small-gain theorems.