The Aizerman Problem for Scalar Differential Equations

摘要

We study the stability of the equilibrium point of a scalar differential equation of an n-th order. We obtain a positive solution to the Aizerman problem for special-type equations. We prove that one can replace the parameter in the real part of the root of the characteristic equation with an arbitrary continuous function, which depends on all phase variables and preserves the global asymptotic stability property.