# Stabilization of Infinite-Dimensional Semilinear Systems with Dissipative Drift

Stabilization of Infinite-Dimensional Semilinear Systems with Dissipative Drift 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# Stabilization of Infinite-Dimensional Semilinear Systems with Dissipative Drift

, Volume 37 (2) – Apr 1, 2023
18 pages

/lp/springer_journal/stabilization-of-infinite-dimensional-semilinear-systems-with-6klkar5eMZ
Publisher
Springer Journals
Copyright © Inc. by 1998 Springer-Verlag New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s002459900075
Publisher site
See Article on Publisher Site

### 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.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Apr 1, 2023

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