Stabilization and decay estimate for distributed bilinear systems

摘要

In this paper, we consider the problem of feedback stabilization for the distributed bilinear system y'(t) = Ay(t) + u(t)By(t). Here A is the infinitesimal generator of a linear C~o semigroup of contractions on a Hilbert space H and B:H -> H is a linear bounded operator. A sufficient condition for feedback stabilization is given and explicit decay estimate is established. Applications to vibrating systems are presented.