About the stability of discrete nonstationary systems of linear Volterra equations

Various type of stability for discrete nonstationary linear systems of Volterra equations are investigated, the peculiarity of which is the dependence of each subsequent state on the entire prehistory of the process. The solutions of the system of linear Volterra equations are represented through Cauchy matrices. Necessary and sufficient conditions for stability and asymptotic stability in the usual and interval statement are established. The presented conditions are expressed in the form of certain restrictions on the norms of Cauchy matrices and on the spectral radius of a special matrix. The stability problems of a perturbed system are considered and estimates are obtained based on the norms of perturbation matrices, which preserve asymptotic stability.