Asymptotic behavior of homogeneous linear recurrent processes and their perturbations

In this paper the impact of small perturbations on asymptotic evolution of homogeneous linear recurrent processes is investigated. Analytical methods for describing homogeneous linear recurrent systems, from convergence, periodicity and boundedness perspective, are presented. These methods are based on Jury Stability Criterion and the classification of the roots of minimal characteristic polynomial in relation to unit disc.