On Frequency Domain Stability for Evolution Equations in Hilbert Spaces via the Algebraic Riccati Equation

We establish Lyapunov type stability for an evolution equation in a Hilbert space by using some energy functions which are obtained via the algebraic Riccati equation. We discuss also briefly the advantages and limitations of this infinite-dimensional extension of a well-known method. Our abstract setting is motivated by some special systems arising in reactor dynamics and retarded differential difference equations.