Aizerman conjectures for a class of multivariate positive systems

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. Here, a number of Aizerman conjectures are shown to be true for a class of internally positive multivariate systems, under a natural generalization of the classical sector condition and, moreover, guarantee positivity in closed loop. These results are stronger and/or more general than existing results. This article relates the obtained results to other, diverse, results in the literature.