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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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