Polynomial Internal and External Stability of Well-posed Linear Systems

We introduce polynomial stabilizability and detectability of well-posed systems in the sense that a feedback produces a polynomial stable C0–semigroup. Using these concepts, the polynomial stability of the given C0–semigroup governing the state equation can be characterized via polynomial bounds on the transfer function. We further give sufficient conditions for polynomial stabilizability and detectability in terms of decompositions into a polynomial stable and an observable part. Our approach relies on recent a characterization of polynomial stable C0–semigroups on a Hilbert space by resolvent estimates.