Almost sure stability of switched stochastic systems with impulsive effects

Based on the matrices, almost sure strong stability with respect to partial variables in It stochastic linear system was studied.

The problems of p-Moment exponential stability and almost sure exponential stability of nonlinear stochastic impulsive systems with Markovian switching are studied.

In view of the character of saturation of output functions of the cellular neural networks, the method decomposing the state to sub-regions is adopted to study almost sure exponential stability on a class delayed cellular neural networks which are in the noised environment.

Some algebraic criterion of almost sure exponential stability are obtained when the disturbance term of the network satisfies the Lipschitz condition.

A method to divide the state space into sub-domains adopted to study almost sure exponential stability over the cellular neural networks under noise environment.

Some sufficient conditions for the 2-th moment exponential stability and almost sure exponential stability are established.

By constructing the new Lyapunov function,some sufficient conditions are obtained and prooved for p-moment exponential stability and almost surely exponential stability.

We have given the comparision criterions of exponential stability,exponential P-stability and almost surely exponential stability,these comparision criterions generalize the corresponding results of Mevel son and Has minskiǐ in [1].