Stability analysis of discrete-time dynamical systems via positive upper aggregated systems

This paper deals with the stability analysis of non-linear and/or large-scale discrete-time dynamical systems by using vector positive definite functions for the construction of a positive upper aggregated system whose stability properties imply analogous properties for the system being studied. In the first part of the paper a rigorous foundation of the approach is presented. The second part is concerned with the stability analysis of non-linear positive discrete-time dynamical systems. Two examples are given to illustrate the application of the results.