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Zero patterns and dominant modes of the state evolutions of autonomous continuous-time positive systems
Abstract\u2014In this paper, the zero pattern properties and
the asymptotic evolution of the trajectories of an autonomous
continuous-time positive system are investigated. To this end, a
normal form for the exponential of a Metzler matrix is provided,
and the concept of \u201cechelon basis\u201d is introduced. By making
use of these two ingredients, the dominant mode of each single
block appearing in the normal form of the exponential matrix is
determined. As a result, the zero pattern as well as the dominant
mode of every state evolution, depending on the zero pattern
of the initial state, can be easily inferred