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Observability of real analytic vector fields on compact manifolds. (English) Zbl 0877.93011

Summary: A smooth vector field on a smooth compact manifold is said to be observable if there exists a smooth \({\mathbb{R}}^{1}\)-valued output function that distinguishes initial states on any time interval. We prove that a real analytic vector field on a compact manifold is observable if and only if its singularities are isolated. The result remains true for \({\mathbb{R}}^{p}\)-valued functions. In this case one has to assume that the set of singular points is \((p-1)\)-dimensional.

MSC:

93B07 Observability
93B29 Differential-geometric methods in systems theory (MSC2000)
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