P0-property and linear inequalities in positive systems analysis (original) (raw)

Abstract

A matrix M ∊ Rn×n is a P0-matrix if every principal minor of M is nonnegative. We use this concept in a generalized form, called row (column)-P0-property, which refers to a finite set of matrices M = {M1,…, MN} ⊂ Rn×n. In the current work, the set M collects matrices of the form Mθ = Aθ − rI, θ = 1,…, N, with Aθ ∊ Rn×n essentially nonnegative and Hurwitz stable, and r < 0. Relying on the P0-property of M, we investigate the existence of nonnegative vectors v ∊Rn (depending on r

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