Asymptotic Properties of a Class of Discrete Time-Varying Systems with Nonnegative Coefficients

摘要

Asymptotic properties of a class of linear discrete time-varying systems with non-negative coefficients are investigated using the classical results on nonnegative matrices and reducibility considerations. Discrete systems with nonnegative coefficients are used in mathematical modeling of economic processes, dynamics of biological populations, in studying Markov chains, etc. For the stationary case, main facts on the limiting behavior of their solutions are easily determined from the classical theorems of Perron and Frobenius. Time-varying systems are far more difficult to investigate and there is no general effective method for describing their asymptotic properties. In this paper, we study time-varying systems, reducing them to autonomous form by special transformation groups that preserve the nonnegativity property.