On the stability of a strongly stabilizing control for degenerate systems in Hilbert spaces

Abstract

In this article, we explain how a recent Lyapunov theorem on stability plays a role in the study of the strong stabilizability problem in Hilbert spaces. We explore a degenerate controlled system and investigate the properties of a feedback control to stabilize such system in depth. The spectral theory of an appropriate pencil operator is used to generate robustness constraints for a stabilizing control.

Keywords

• stabilization of systems by feedback
• operators theory
• degenerate systems
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