In this paper, we investigate a model‐based periodic event‐triggered control framework for continuous‐time stochastic nonlinear systems. In this framework, an auxiliary approximate discrete‐time model of stochastic nonlinear systems is constructed in the controller module, which is utilized not only to design a discrete‐time controller but also as a state predictor within trigger intervals. This discrete controller design approach, the strategy of state prediction, and the periodic detection strategy for the trigger rule not only provide a manner of more direct and easier implementation on the digital platform but also effectively reduce the communication load while a satisfactory control performance is maintained. Additionally, the mean‐square exponentially stabilization for continuous‐time stochastic nonlinear systems is achieved, in which a guideline for determining the maximum admissible sampling period is provided and the periodic event trigger rule is designed. The final numerical simulation also supports the effectiveness of our proposed framework.

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In this paper, a stabilization scheme for a class of continuous-time nonlinear Markov jump systems is investigated by sampled-data control mechanism. This stabilization scheme is given in the form of a discrete-time state feedback controller which is designed based on the approximate discrete-time model (ADTM) of the original continuous-time system via the discrete-time design method.During the process of controller design, an appropriate iteration step size is selected for the ADTM to restore the missing intersampling data due to the sampling characteristics, and this provides the iteration solutions of ADTM to the controller. The introduction of the iteration step size achieves a perfect tradeoff between calculation precision and control cost which not only guarantees the calculation precision of the ADTM, but also reduces sampling frequency effectively. Subsequently, we analyze the consistency condition between the continuous-time nonlinear Markov jump systems and its ADTM, and give the criterion of the mean-square exponential stability of the system. Based on this criterion, we prove the mean-square exponential stability of the closed-loop sampled-data system with the designed discrete-time state feedback controller.Finally, the feasibility and effectiveness of this scheme are clearly verified by a numerical example.

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