A simple three-state system with two inputs is considered. The system's controllability is determined using properties of vector-valued quadratic forms. The quadratic structure is then used as the basis for the design of a homogeneous, discontinuous, stabilising feedback controller. The paper should be seen as an attempt to relate controllability of a system from a point to stabilisability of the system to the same point.

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Last Updated: Fri Apr 25 10:11:57 2025