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. Here, a number of Aizerman conjectures are shown to be <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">true</i> for a class of internally positive multivariate systems, under a natural generalisation of the classical sector condition and, moreover, guarantee positivity in closed loop. These results are stronger and/or more general than existing results. The paper relates the obtained results to other, diverse, results in the literature.