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Stabilization of infinite-dimensional semilinear systems with dissipative drift. (English) Zbl 1041.93553
Summary: In this paper we study feedback stabilization for distributed semilinear control systems $$\dot{x}(t) = Ax(t) + u(t){\mathcal B}(x(t))$$. Here, $$A$$ is the infinitesimal generator of a linear $$C_0$$ -semigroup of contractions on a real Hilbert space $$H$$ and $${\mathcal B}$$ 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.

##### MSC:
 93D15 Stabilization of systems by feedback 47N70 Applications of operator theory in systems, signals, circuits, and control theory 93C25 Control/observation systems in abstract spaces
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