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arXiv · 2604.12065

On Asymptotic and Finite-Time Stabilization of Bilinear Systems

Mohamed Ouzahra
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Abstract

This manuscript addresses the analysis and design of feedback laws for the stabilization of bilinear control systems in infinite-dimensional spaces. It first examines weak, strong, and polynomial stabilization within a Hilbert space framework, emphasizing the role of observability conditions. It then studies exponential stabilization in Banach spaces, highlighting the additional challenges arising from the lack of a Hilbertian structure. Finally, it introduces finite-time stabilization, presenting recent results and open problems within the broader context of nonlinear infinite-dimensional control theory. Several applications are also discussed.

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Mohamed Ouzahra. 2026-04-13. On Asymptotic and Finite-Time Stabilization of Bilinear Systems. https://arxiv.org/abs/2604.12065

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