Box invariant sets are box-shaped positively invariant sets. We show that box invariants are computable for a large class of nonlinear and hybrid systems. The technique for computing these invariants is based on nonlinear constraint solving. This paper also shows that the class of multiaffine systems, which has been used successfully for modeling and analyzing regulatory and biochemical reaction networks, can be generalized to the class of monotone and quasi-monotone systems without losing any of its nice properties.
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