Abstract In this paper, the problem of global finite-time stabilization of bilinear control systems by means of homogeneous feedback law is investigated. We prove under some reasonable assumptions on the operators A and B that continuous bounded and discontinuous unbounded feedbacks stabilize globally in finite-time the closed loop system. For illustrative, the examples of heat, Schrodinger and transport equations are considered where homogeneous stabilizing feedback is built for these systems.

中文翻译：

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基于齐次反馈定律的双线性系统全局有限时间镇定。一些 PDE 的应用

摘要 本文研究了基于齐次反馈律的双线性控制系统全局有限时间镇定问题。我们在对算子 A 和 B 的一些合理假设下证明，连续有界和不连续无界反馈在闭环系统的有限时间内全局稳定。为了说明，考虑了热、薛定谔和传输方程的例子，其中为这些系统建立了均匀的稳定反馈。