Stability of systems of Ito linear differential equations with delays

Abstract

The questions of instant stability of systems of linear differential equations Ito with delays based on the theory of positively reversible matrices are investigated. The ideas and methods developed by N. V. Azbelev and his students to investigate the sustainability of deterministic linear functional--differential equations are used for this. Are brought sufficient conditions $2p$--stability $(1\le p <\infty)$ systems of linear differential Ito equations with delays in terms of positive reversibility of the matrices, built according to the parameters of the source system. The fulfillment of these conditions for specific equations is checked.