Practical stability with respect to a part of variables of stochastic differential equations

Abstract

In this paper, practical stability with respect to a part of the variables of nonlinear stochastic differential equations is studied. The analysis of the global practical uniform asymptotic stability, the global practical uniform pth moment exponential stability, as well as the global practical uniform exponential stability with respect to a part of the variables of SDEs are carried out by using the Lyapunov techniques. Some illustrative examples to show the usefulness of the stability with respect to a part of variables notion are also provided.