Pei Cheng

On Input-to-State Stability of Impulsive Stochastic Systems with Time Delays

This paper is concerned with pth moment input-to-state stability (p-ISS) and stochastic input-to-state stability (SISS) of impulsive stochastic systems with time delays. Razumikhin-type theorems ensuring p-ISS/SISS are established for the mentioned systems with external input affecting both the continuous and the discrete dynamics. It is shown that when the impulse-free delayed stochastic dynamics are p-ISS/SISS but the impulses are destabilizing, the p-ISS/SISS property of the impulsive stochastic systems can be preserved if the length of the impulsive interval is large enough. In particular, if the impulse-free delayed stochastic dynamics are p-ISS/SISS and the discrete dynamics are marginally stable for the zero input, the impulsive stochastic system is p-ISS/SISS regardless of how often or how seldom the impulses occur. To overcome the difficulties caused by the coexistence of time delays, impulses, and stochastic effects, Razumikhin techniques and piecewise continuous Lyapunov functions as well as stochastic analysis techniques are involved together. An example is provided to illustrate the effectiveness and advantages of our results.

Almost sure exponential stability of stochastic neural networks

This paper is concerned with the almost sure exponential stability analysis for stochastic neural network systems. Based on the methods of Lyapunov functions, some criteria for the almost sure exponential stability of these stochastic systems are derived, which show that noises can be used to stabilize unstable neural networks. Our results complete the recent works. Two examples are given to illustrate the effectiveness of the obtained results.