Finite-time Stability Analysis for Random Nonlinear Systems

TL;DR

This paper develops a Lyapunov-based method to analyze finite-time stability in probability for nonlinear systems modeled by random differential equations, providing theoretical guarantees and practical examples.

Contribution

It introduces a novel Lyapunov theorem for finite-time attraction in probability for stochastic nonlinear systems, with less restrictive assumptions.

Findings

Established conditions for finite-time attraction in probability.

Proved existence and uniqueness of solutions for RDEs.

Validated the approach with two illustrative examples.

Abstract

This paper presents an analysis approach to finite-time attraction in probability concerns with nonlinear systems described by nonlinear random differential equations (RDE). RDE provide meticulous physical interpreted models for some applications contain stochastic disturbance. The existence and the path-wise uniqueness of the finite-time solution are investigated through nonrestrictive assumptions. Then a finite-time attraction analysis is considered through the definition of the stochastic settling time function and a Lyapunov based approach. A Lyapunov theorem provides sufficient conditions to guarantee finite-time attraction in probability of random nonlinear systems. A Lyapunov function ensures stability in probability and a finiteness of the expectation of the stochastic settling time function. Results are demonstrated employing the method for two examples to show potential of the proposed technique.