Design of event-based sliding mode controller with logarithmic quantized state measurement and delayed control update

This paper concerns with the robust stabilization of a perturbed linear time-invariant (LTI) single-input single-output (SISO) system based on event-based/ event-triggered sliding mode control (SMC) with logarithmic quantized state measurement. This technique is expected to reduce communication traffic in control networks with the assurance of robust stability against the quantization error and external perturbations. In practice, delay is inevitable in the control computation during the implementation of the control law. The proposed event-triggering mechanism is analysed for the two scenarios: with delay and without delay in control computation. The robust stability of the uncertain system is ensured with the external disturbances, the error introduced by the quantization process and delay encountered in control computation with the proposed event-based SMC. The lower bound of minimum inter event execution time is derived to ensure the Zeno free behaviour. To show the effect of delay on the triggering mechanism, the maximum bound of the delay is obtained to guarantee the Zeno free behaviour with the robust stability of the closed loop system. An example of a mechanical system is simulated and results are shown to validate the effectiveness of the proposed methodology.