Output contraction analysis of discrete-time nonlinear systems with an application to RNNs.

Abstract

This paper studies output contraction of discrete-time nonlinear systems characterized by the exponential convergence of any two outputs. Additionally, the notion of incrementally asymptotic output stability is also introduced. The first result establishes a connection between the output contraction of discrete-time nonlinear systems and the output exponential stability of the associated variational system. Subsequently, sufficient conditions for the output contraction and the incrementally asymptotic output stability are derived. As an application of the developed results, the output contraction of recurrent neural networks is analyzed depending on their dynamic structure. Finally, numerical examples are provided to verify the obtained results.