The theories of controllability (from a state) and stabilisability (to a state) are among the most fundamental in control theory. Anyone seeing the definitions of these notions for the first time and possessing no preexisting socio-academic bias would think that these subjects are very closely linked. Such a (fictitious) person would then be surprised to see that the literature on these subjects is virutally disjoint. The theory of controllability is geometric and is about Lie algebras of vector fields and the like. The theory of stabilisability is analytic in nature and is about Lyapunov functions and the like.
In this talk I will say a few words about these subjects, attempting to strip away the fact that they have developed along almost entirely separate lines. I will focus on a few simple questions and some results (some obvious and some not) related to these questions that indicate that the distinctions we see in these areas of research are not real, but human-made.
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