1. Z. Liu, N. Ozay, and E.D. Sontag. On the non-existence of immersions for systems with multiple omega-limit sets. In Proceedings of IFAC 2023 World Congress, pages 81-85, 2023. [PDF] Keyword(s): linear systems, nonlinear systems, observables, Koopman embedding, duality. Abstract:

   Linear immersions (or Koopman eigenmappings) of a nonlinear system have wide applications in prediction and control. In this work, we study the existence of one-to-one linear immersions for nonlinear systems with multiple omega-limit sets. For this class of systems, existing work shows that a discontinuous one-to-one linear immersion may exist, but it is unclear if a continuous one-to-one linear immersion exists. Under mild conditions, we prove that systems with multiple omega-limit sets cannot admit a continuous one-to-one immersion to a class of systems including linear systems.

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