Box invariance in biologically-inspired dynamical systems

Authors:
Alessandro Abate;Ashish Tiwari;Shankar Sastry
Affiliations:
Department of Aeronautics and Astronautics, Stanford University, CA, United States;Computer Science Laboratory, SRI International, Menlo Park, CA, United States;Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, United States
Venue:
Automatica (Journal of IFAC)
Year:
2009

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Abstract

A dynamical system is box invariant if there exists a box-shaped positively invariant region. We show that box invariance can be checked in cubic time for linear and affine systems, and that it remains decidable for classes of nonlinear systems of interest (with polynomial structure). We present results on the robustness of box invariance for linear systems using spectral properties of Metzler matrices. We also present sufficient conditions for establishing box invariance of switched and hybrid systems. In general, we argue that box invariance is a characteristic of many biologically-inspired dynamical models.