Two of the most fundamental concepts in control theory are controllability (roughly, can one steer from one state to another) and stabilisability (roughly, can one render a possibly unstable state stable using control). The topic of controllability is well studied in the framework of geometric control theory. The topic of stabilisability, however, while well studied in its own right by analytical Lyapunov-style methods, is not really a part of modern geometric control theory. In this talk we present the ideas of controllability and stabilisability and very briefly describe the history of these subjects. Finally, we describe some recent efforts to bring the theory of stabilisability into the fold of geometric control theory by relating it precisely to controllability.

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