Bounds on the state vector growth rate in stochastic dynamical systems

TL;DR

This paper derives simple bounds on the mean growth rate of the state vector in stochastic linear systems modeled with idempotent algebra, providing analysis of the bounds' accuracy and numerical evaluations.

Contribution

It introduces new bounds for the growth rate in stochastic systems using idempotent algebra and analyzes their accuracy.

Findings

Bounds effectively estimate the growth rate

Error analysis shows bounds' reliability

Numerical results validate theoretical bounds

Abstract

A stochastic dynamical system represented through a linear vector equation in idempotent algebra is considered. We propose simple bounds on the mean growth rate of the system state vector, and give an analysis of absolute error of a bound. As an illustration, numerical results of evaluation of the bounds for a test system are also presented.