A note on stabilization with saturating feedback
The authors consider a distributed parameter control system \[ \dot x= Ax+ Bu, \] where \(A\) generates a \(C_0\) contractions semigroup on a Hilbert space \({\mathcal H}\) and \(B\) is a linear bounded operator from another Hilbert space \({\mathcal U}\) to \({\mathcal H}\). The basic assumption is that \(u= -B^* x\) is an asymptotically stabilizing feedback. Then they prove that the system can be stabilized even with a saturating feedback (i.e., a feedback subject to the restriction \(\|u\|\leq 1\)). In the last section of the paper the authors point out that the continuity assumption about \(B\) can be relaxed.
scientific article; zbMATH DE number 1882980