Stabilization of Infinite-Dimensional Semilinear Systems with Dissipative Drift

Abstract.

In this paper we study feedback stabilization for distributed semilinear control systems $\dot{x}(t) = Ax(t) + u(t){\cal B}(x(t))$ . Here, A is the infinitesimal generator of a linear C ₀ -semigroup of contractions on a real Hilbert space H and ${\cal B}$ is a nonlinear operator on H into itself. A sufficient ad-condition is provided for strong feedback stabilization. The result is illustrated by means of partial differential systems.