Exponential stabilization of hyperbolic systems with nonlinear, unbounded perturbations—riccati operator approach

Abstract

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 unstruc¬tured 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

Keywords:

• Abstract differential equations
• nonlinear unstructured and unbounded perturbations
• stabilization
• Riccati equations
• Kirchhoff plate

AMS(MOS)::

• 49

^*Research partially supported by the NSF Grant DMS–8301668 and by the AFOSR 89–0511

^*Research partially supported by the NSF Grant DMS–8301668 and by the AFOSR 89–0511

Notes

^*Research partially supported by the NSF Grant DMS–8301668 and by the AFOSR 89–0511