Stability analysis for a class of nonlinear time-changed systems

Abstract

This paper investigates the stability of a class of differential systems time-changed by $E_t$ which is the inverse of a $\beta$-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, $p$th moment asymptotic stability and $p$th 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.