Semi-global exponential stability of stochastic nonlinear functional sampling systems by emulation approach

In this paper, the semi-global exponential stability is studied for the stochastic nonlinear functional systems by emulation of sampled-data controller. In consideration of the stochastic factor, a novel definition of the right and upper Dini's derivative of the constructed functional is given. Based on this novel definition, combining with stochastic analysis techniques and Lyapunov method, some sufficient criteria for the semi-global exponential stability of the stochastic nonlinear functional systems by suitably fast sampling are given. As a special case, a class of stochastic nonlinear functional systems with multiple time delays is studied and two coefficient type theorems that lead to the semi-global exponential stability of the sampling system are derived. Finally, a practical application about parallel active suspension systems with time delay and stochastic disturbance is discussed at length and the corresponding numerical example is given to illustrate the feasibility of the theoretical results.