Abstract
In this chapter, the theory developed so far is applied to specific classes of systems. In particular, we obtain formulas and/or estimates for the invariance entropy of control sets of scalar control-affine systems, uniformly expanding systems, inhomogeneous bilinear systems given by differential equations, and projective systems (which are control-affine systems on real projective space \({\mathbb{P}}^{d}\) induced by bilinear systems on \({\mathbb{R}}^{d+1}\)).
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Notes
- 1.
The letters “gh” are supposed to stand for “geodesic hull”, though we mean something slightly different here.
- 2.
The round metric gr on S d is the Riemannian metric induced by the Euclidean metric of \({\mathbb{R}}^{d+1}\) , that is, \(g_{x}^{r}(v,w) =\langle v,w\rangle =\sum _{i}v_{i}w_{i}\) for all x ∈ S d and \(v,w \in T_{x}\mathrm{{S}}^{d}\) , where T xS d is identified with a linear subspace of \({\mathbb{R}}^{d+1}\).
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Kawan, C. (2013). Examples. In: Invariance Entropy for Deterministic Control Systems. Lecture Notes in Mathematics, vol 2089. Springer, Cham. https://doi.org/10.1007/978-3-319-01288-9_7
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