Exponential stability with respect to part of the variables for a class of nonlinear stochastic systems with Markovian switchings

This paper deals with the exponential stability problem with respect to part of the variables of a class of nonlinear stochastic systems for three classes of Markovian switching processes. The methodologies of stability of stochastic hybrid systems and stability with respect to part of the variables based on Lyapunov methods are combined to find sufficient conditions of the exponential yp-stability for a class of nonlinear stochastic systems. Moreover, the detailed analysis and criteria of exponential mean square y-stability based on LMI methodology are also given for the case of linear systems.