Time-domain Boundedness of Noise-to-State Exponentially Stable Systems

TL;DR

This paper establishes the time-domain boundedness of noise-to-state exponentially stable systems, providing insights into how long solutions remain within the domain of attraction and their behavior if they escape.

Contribution

It introduces a method to estimate the lower bound function for the duration solutions stay within the domain of attraction in noise-to-state exponentially stable systems.

Findings

Proves time-domain boundedness of such systems

Provides lower bound estimates for solution duration

Enhances understanding of system behavior upon escape from attraction domain

Abstract

In this paper we prove the time-domain boundedness for noise-to-state exponentially stable systems, and further make an estimation of its lower bound function, which allows to answer the question that how long the solution of a stochastic noise-to-state exponentially stable system stays in the domain of attraction and what happens with it if it escapes from this region for a while. The results will complement the probability-domain boundedness of noise-to-state exponentially stable systems, and provide a new insight into noise-to-state exponential stability.