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arXiv · 2201.05014

Control Sets for Affine Systems, Spectral Properties and Projective Spaces

Fritz Colonius·Alexandre J. Santana·Juliana Setti
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Abstract

For affine control systems with bounded control range the control sets, i.e., the maximal subsets of complete approximate controllability, are studied using spectral properties. For hyperbolic systems there is a unique control set with nonvoid interior and it is bounded. For nonhyperbolic systems, these control sets are unbounded. In an appropriate compactification of the state space there is a unique chain control set and the relations to the homogenous part of the control system are worked out.

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Fritz Colonius, Alexandre J. Santana, Juliana Setti. 2022-01-13. Control Sets for Affine Systems, Spectral Properties and Projective Spaces. https://arxiv.org/abs/2201.05014

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