The Nehari problem for nonexponentially stable systems (Q1265580)

The authors consider a state-space solution to the Nehari problem in terms of the generating operators \(A,B,C\). The assumptions that \(A\) generates an exponentially stable \(C_0\)-semigroup and that the Hankel operator is compact, which are used for infinite-dimensional problems, are not supposed. The aim of this paper is to derive an explicit parametrization of all solutions to the Nehari extension problems in terms of \(A,B,C\) operators for which the corresponding linear system is not exponentially stabilizable. The proofs are explicitly given and the paper is recommended to mathematicians and engineers working in the field of infinite-dimensional linear controlled systems.