Finite-time boundedness of sliding mode control under periodic event-triggered strategy

This article investigates the problem of sliding mode control (SMC) for continuous-time systems under the requirement of finite-time boundedness (FTB), in which the state signals are periodically sampled and transmitted to the controller according to the pre-designed event-triggering condition. A key issue is how to utilize the less available state information to achieve the FTB of the closed-loop system. To this end, the continuous-time SMC law is changed into an implementable form dependent on the available sampled state via event triggering transmission. It is shown that the state trajectory of the controlled system can be driven onto the specified sliding surface before the given finite time, and then, remain within a domain around this sliding surface. Due to the characteristic of the periodic event-triggered scheme (ETS), the known partitioning strategy on the SMC with FTB is infeasible for this present case. Instead, we shall analyze the FTB of the closed-loop system over the whole given time, meanwhile, a selection condition on the robust term is given via the given time parameter. Finally, the numerical simulation results are provided to illustrate the proposed periodical event-triggered SMC scheme.