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This paper reports on the latest developments in taxonomy theory originally developed for dynamic systems represented by ordinary differential equations constrained by algebraic equations (DAEs). It gives some new results on the behavior of a second order state constrained system. It shows that the interplay between an unstable system and the hard limit can result generically in stable non-smooth limit cycles. These results are of particular importance for Hopf bifurcations which occur near the state limit since they point towards the possibility of stable operation even after a subcritical Hopf bifurcation has occured.
Jiang et al. (Tue,) studied this question.