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The Concept of Box Invariance for special classes of Dynamical Systems

In this paper we introduce the concept of Box Invariance for dynamical systems. The notion has been inspired by experience with models drawn from Biology; in fact, we claim that Box Invariance is a characteristic of many biologically-inspired dynamical models. Moreover, Box Invariance property turns out to be quite useful for formally verifying safety properties of dynamical systems. Effective characterization of this notion, the study of the dynamical properties it subsumes and a comparison with related concepts in the literature will be investigated for the case of linear and affine systems. Applications from the biological world will be provided throughout the manuscript.