Exponential decay for distributed bilinear control systems with damping

Abstract

Let Ω be a bounded open domain in ℝ N ,A an unbounded, selfadjoint, positive and coercive linear operator onL 2 (Ω). We consider feedback stabilization for the distributed bilinear control systemy″(t)+Ay(t)+Dy′(t)+u(t)By(t)=0, whereD andB are linear bounded operators fromL 2(Ω) toL 2(Ω). Under suitable assumptions onB andD, a nonlinear feedback ensuring uniform exponential decay of solutions is given. Various applications to vibrating processes are presented.