Criteria for practical stability in the pth mean of nonlinear stochastic systems

A new concept, practical stability in the pth mean, is proposed for nonlinear stochastic systems. By using the Lyapunov-like functions and the basic comparison principle for stochastic systems, criteria are established for various types of practical stability in the pth mean of nonlinear stochastic systems. These criteria make it possible to determine the practical stability in the pth mean of the nonlinear stochastic systems by testing the practical stability of the corresponding auxiliary deterministic systems.