Stochastic sampling control for a class of nonlinear continuous-time systems

In this paper, the problem of stochastic sampling control for a class of nonlinear continuous-time systems is investigated. For the simplicity of calculation, only two different sampling periods are considered whose occurrence probabilities are given constants and satisfy Bernoulli distribution, which can be further extended to the case with multiple stochastic sampling periods. By using the input delay approach and the Takagi-Sugeno (T-S) fuzzy system method, a class of nonlinear continuous-time systems with stochastic sampling is transformed into a continuous-time T-S fuzzy system with time-varying delays and the stochastic parameters. Based on Lyapunov stability theory, a mean square asymptotic stability condition for the closed-loop T-S fuzzy system is proposed. Furthermore, the controller design method is given in terms of LMI. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.