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