Stability analysis for a class of nonlinear time-changed systems - Qiong Wu (Cogent Mathematics, 2016)
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.