Polynomial internal and external stability of well-posed linear systems

Abstract

We introduce polynomial stabilizability and detectability of wellposed systems in the sense that a feedback produces a polynomially 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 a recent characterization of polynomially stable C0-semigroups on a Hilbert space by resolvent estimates.