Event-Triggered Sliding Mode Control for Delta Operator Systems

The paper presents an event-triggering based sliding mode control law for delta operator systems with disturbance. The discrete domain representation of a system using shift operator becomes numerically ill-conditioned at very high sampling rates. To circumvent this problem, the system is represented using delta operator. The delta operator creates a rapprochement between continuous-time and discrete-time system model at very high sampling rates. A discrete-time sliding mode (DTSM) control law is developed to achieve robustness against external disturbances. Further to reduce the resource utilization, an event-triggered DTSM control law is proposed such that the closed loop system is stable. Due to the inherent discrete nature of the control there is no accumulation of triggering instants at any instant of time. Hence the zeno free execution of the control updating instants is always guaranteed. Simulation results are also shown to illustrate the effectiveness of the proposed method.