Strong stability of quasi-affine transforms of contraction semigroups and the steady-state Riccati equation (Q798288)

This paper studies strong stability of the class of strongly continuous Hilbert space semigroups which are quasi-affine transforms of contraction semigroups. Sufficient conditions for such a semigroup to be approximately strong stable are given. Application to the stabilizability problem of Hilbert space semigroups, using a feedback involving a solution of the steady-state Riccati equation are made. Our key tool is the generalization of the \textit{J. P. LaSalle} [J. Differ. Equations 4, 57-65 (1968; Zbl 0159.120)] invariance principle by \textit{J. K. Hale} [J. Math. Anal. Appl. 26, 39-59 (1969; Zbl 0179.133)].