Aizerman Conjectures for a class of multivariate positive systems

Abstract

The Aizerman Conjecture predicts stability for a class of nonlinear control systems on the basis of linear system stability analysis. The conjecture is known to be false in general. This paper will discuss a number of related Aizerman conjectures and will show that they are true for a certain class of internally positive multivariate systems, under a natural generalisation of the classical sector condition and moreover guarantee positive invariance. The results are stronger or more general than existing results. The paper will also relate the obtained results to other, diverse, results in the literature.