Reducibility by Moments of Linear Impulse Markov Dynamical Systems with Almost Constant Coefficients

This paper deals with linear impulse dynamical systems on ℝ^d whose parameters depend on an ergodic piece-wise constant Markov process with values from some phase space 𝕐 and on a small parameter ɛ. Trajectories of Markov process x(t,y)∈ ℝ^d satisfy a system of linear differential equations with close to constant coefficients on its continuity intervals, while its phase coordinate changes discontinuously when Markov process switching occur. Jump sizes depend linearly on the phase coordinate and are proportional to the small parameter ɛ. We propose a method and an algorithm for choosing the base 𝔹(t,y) of the space ℝ^d that provides approximation of average phase trajectories E{x(t,y)} by a solution of a system of linear differential equations with constant coefficients.