Positive invertibility of matrices and stability of Itô delay differential equations

Abstract

We study the global exponential p-stability (1 ≤ p < ∞) of systems of Itô nonlinear delay differential equations of a special form using the theory of positively invertible matrices. To this end, we apply a method developed by N.V. Azbelev and his students for the stability analysis of deterministic functional-differential equations. We obtain sufficient conditions for the global exponential 2p-stability (1 ≤ p < ∞) of systems of Itô nonlinear delay differential equations in terms of the positive invertibility of a matrix constructed from the original system. We verify these conditions for specific equations.