Open problems in controllability and stabilisability of analytic systems are
discussed. In particular, questions like, ``Can controllability and/or
stabilisability be tested by solving algebraic equations?'' and, ``What is
the relationship between controllability *from* a state and
stabilisability *to* the same state?'' are discussed. A main idea is
a rethinking of how one might examine stabilisability by connecting it to
controllability.

For analytic systems, local obstructions to controllability and stabilisability should be determined by the germ of the system at the prescribed state. A means of characterising these germs in a systematic manner is presented.

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Last Updated: Tue Jun 18 09:16:15 2024