Multi-dimensional uncertain differential equation is a tool to model an multi-dimensional dynamic system. Furthermore, stability has significant role in the field of equations because it can be describe effect initial value on solution equation. Hence, concept almost sure presented concerning this paper. Moreover, theorem, that condition, derived judge whether surely stable or not. Additionally...

This paper is mainly concerned with whether the almost sure exponential stability of stochastic differential equations (SDEs) is shared with that of a numerical method. Under the global Lipschitz condition, we first show that the SDE is pth moment exponentially stable (for p ∈ (0, 1)) if and only if the stochastic theta method is pth moment exponentially stable for a sufficiently small step siz...

In this paper, we study the almost sure stability of discretetime jump linear systems with a finite-state Markov-form process. A general condition for almost sure stability, which is a necessary and sufficient condition for (scalar) one-dimensional systems, is derived. Many simpler testable sufficient conditions for almost sure stability are derived from this sufficient condition.