Stabilization of Infinite-Dimensional Semilinear Systems with Dissipative Drift

In this paper we study feedback stabilization for distributed semilinear control systems \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\dot{x}(t) = Ax(t) + u(t){\cal B}(x(t))$ \end{document} . Here, A is the infinitesimal generator of a linear C0 -semigroup of contractions on a real Hilbert space H and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\cal B}$ \end{document} 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.