Comparison Principle and Stability of General Continuous Time Markov Jump System

The comparison principle for general continuous time nonlinear Markov jump system is established. Later, using the comparison principle, we obtain some stability criterion, including stability in probability, uniformly stability in probability, asymptotic stability in probability, uniformly asymptotic stability in probability, pth moment stability, pth moment uniformly stability, pth moment asymptotic stability, pth moment uniformly asymptotic stability and pth moment exponentially of such equations. And a sufficient criterion is proposed which can be verified easily. A numerical example is given to show how to use the criterions.