Stability of hybrid systems
Hybrid systems combine discrete and continuous behavior. We study properties of trajectories of a rectangular hybrid system in which the discrete state goes through a loop. This system is viable if there exists an infinite trajectory starting from some state. We show that the system is viable if and only if it has a limit cycle or fixed point. The set of fixed points is a polyhedron. The viability kernel may not be a polyhedron. However, under a “controllability” condition, the viability kernel is a polyhedron.
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