Feedback boundary control problems for linear semigroups (Q1072982)

The authors consider the problem of unbounded perturbations of generators of strongly continuous semigroups. The perturbation takes the form AB where A is the infinitesimal generator of a strongly continuous semigroup and B is a linear bounded operator. This type of perturbation is motivated by the application of boundary feedback control to a partial differential equation. They obtain sufficient conditions for \(A+AB\) to generate a strongly continuous semigroup, and give an abstract semigroup formulation of the boundary control problem. Surprisingly the authors seem to be unaware of the related work by \textit{D. Salamon} on the same problem [see Control and observation of neutral systems, Res. Notes Math. 91 (1984; Zbl 0546.93041) and Distributed parameter systems, Proc. 2nd Int. Conf., Vorau/Austria 1984, Lect. Notes Control Inf. Sci. 75, 324-339 (1985; Zbl 0577.93038)], despite the fact that two were present at the conference loc. cit. The results are very similar indeed.