Periodic event-triggered sliding mode control

In this paper, we propose the periodic event-triggering based design of sliding mode control (SMC) for the linear time-invariant (LTI) systems. In this technique, the triggering instants are generated by a triggering mechanism which is evaluated periodically at those time instants when the state measurements are available. So, the continuous state measurement, as it is usually needed in the continuous event-triggering strategy, is no longer required in this proposed triggering strategy. The main advantages of this triggering mechanism are: (1) a uniform positive lower bound for the inter event time is guaranteed and (2) this technique is more economical and realistic than its continuous counterpart due to the relaxation of continuous measurements. In this work, we use SMC to design the periodic event-triggering condition where SMC is designed in such a way that it allows periodic evaluation of triggering rule while guaranteeing the robust performance of the system. Moreover, an upper bound of the sampling period for the periodic measurements is also obtained in this design. Finally, the simulation results are given to demonstrate the design methodology and performance of the system with the proposed event-triggering strategy.