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 C ₀-semigroup. Using these concepts, the polynomial stability of the given C ₀-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 C ₀-semigroups on a Hilbert space by resolvent estimates.

Mathematics Subject Classification (2010). Primary: 93D25. Secondary: 47A55, 47D06, 93C25, 93D15.