Remarks on random dynamical systems with inputs and outputs and a small-gain theorem for monotone RDS

TL;DR

This paper introduces a new concept of random dynamical systems with inputs and outputs and presents a generalized small-gain theorem for monotone systems, extending deterministic results to stochastic settings.

Contribution

It proposes a novel framework for random dynamical systems with inputs/outputs and generalizes the small-gain theorem to monotone stochastic systems.

Findings

New notion of RDS with inputs and outputs

Generalized small-gain theorem for monotone RDS

Extension of deterministic results to stochastic systems

Abstract

This note introduces a new notion of random dynamical system with inputs and outputs, and sketches a small-gain theorem for monotone systems which generalizes a similar theorem known for deterministic systems.