Kvalheim, Matthew D.2024-10-282024-10-282024-06-05https://doi.org/10.48550/arXiv.2312.16752http://hdl.handle.net/11603/36730The author's extensions of Brockett's and Coron's necessary conditions for stabilizability are shown to be independent in the fiber bundle picture of control, but the latter is shown to be stronger in the vector bundle picture if the state space is orientable and the Cech-Euler characteristic of the set to be stabilized is nonzero.15 pagesen-USThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.Electrical Engineering and Systems Science - Systems and ControlMathematics - Differential GeometryComputer Science - Systems and ControlMathematics - Optimization and ControlMathematics - Algebraic TopologyText