Asymptotic Stability of 3D Stochastic Positive Linear Systems with Delays

Abstract

The article emphasizes that 3D stochastic positive linear system with delays is asymptotically stable and depends on the sum of the system matrices and at the same time independent on the values and numbers of the delays. Moreover, the asymptotic stability test of this system with delays can be abridged to the check of its corresponding 2D stochastic positive linear systems without delays. Many theorems were applied to prove that asymptotic stability for 3D stochastic positive linear systems with delays are equivalent to 2D stochastic positive linear systems without delays. The efficiency of the given methods is illustrated on some numerical examples.
 HIGHLIGHTS
 
 Various theorems were applied to prove the asymptotic stability of 3D stochastic positive linear system with delays. Moreover, this system can be reduced to 2D stochastic positive linear system without delays
 Asymptotic stability of 3D stochastic positive linear systems with delays depends on the summation of system matrices and independent on numbers and values of delays for that system
 The principal minors and the coefficients for characteristic polynomials of 3D stochastic linear systems were applied to demonstrate the asymptotic stability when they are all positive