Stability analysis for a class of nonlinear time-changed systems

2016/02/23 by Qiong Wu, Wu, Qiong · 1 citation
Engineering · Mathematics · #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stability and Control of Uncertain Systems

paper · pdf · doi:10.48550/arxiv.1602.07342

openalex publication_date 2016/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper investigates the stability of a class of differential systems time-changed by E_t which is the inverse of a β-stable subordinator. In order to explore stability, a time-changed Gronwall's inequality and a generalized Itô formula related to both the natural time t and the time-change E_t are developed. For different time-changed systems, corresponding stability behaviors such as exponential sample-path stability, pth moment asymptotic stability and pth moment exponential stability are investigated. Also a connection between the stability of the time-changed system and that of its corresponding non-time-changed system is revealed.

Cited by

• Stability of stochastic differential equations with respect to time-changed Brownian motions

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