Positive Invertibility of Matrices and Exponential Stability of Impulsive Systems of Itô Linear Differential Equations with Bounded Delays

Abstract

Basing on the theory of positively invertible matrices, we study certain questions of the exponential 2p-stability (1 ≤ p < ∞) of systems of Itô linear differential equations with bounded delays and impulse actions on certain solution components. We apply the ideas and methods developed by N.V. Azbelev and his followers for studying the stability of deterministic functional differential equations. For the systems of equations mentioned above, we establish sufficient conditions for the exponential 2p-stability (1 ≤ p < ∞) stated in terms of the positive invertibility of matrices constructed from parameters of these systems. We verify the feasibility of these conditions for certain specific systems of equations.