Exponential Stabilization of Hyperbolic Systems with Nonlinear, Unbounded Perturbations—Riccati Operator Approach
Abstract differential equations with nonlinear unstructured perturbations represented by unbounded nonlinear operators are considered. It is shown that such system can be uniformly locally stabilized by the feedback operator (also unbounded) which is constructed via the solution of an appropriate Riccati Equation. Abstract results are applied to the model of a Kirchhoff plate with nonlinear unstructured boundary perturbations. In this case, it is proved that the energy of the solutions with boundary (moment) feedback based on Riccati operator decays uniformly (locally) to zero. © 1991, Taylor & Francis Group, LLC. All rights reserved.
Lasiecka, I. (1991). Exponential Stabilization of Hyperbolic Systems with Nonlinear, Unbounded Perturbations—Riccati Operator Approach. Applicable Analysis, 42 (1-4), 243-261. https://doi.org/10.1080/00036819108840045