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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.

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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