Disturbance Rejection for Uncertain Discrete-Time Linear Systems Through Event-Triggered Control

This work addresses the problem of disturbance rejection for discrete-time linear uncertain systems through an event-triggered control. Assuming that the disturbances are generated by an exosystem and only the output of the plant is available for measurement, an observer-based event-triggered controller to ensure the robust asymptotic stability and the disturbance rejection in steady-state is proposed. Considering this setup, LMI-based conditions that ensure the perfect asymptotic disturbance rejection are derived and a convex optimization problem is proposed to systematically compute the event-triggering strategy parameters aiming at reducing the control updates. Since the perfect asymptotic rejection of non-constant disturbances degenerates to periodic (i.e. time-triggered) updates of the control signal in steady-state, a practical disturbance rejection mechanism based on a relaxed triggering criterion and a corresponding convex optimization problem is also proposed. Numerical examples illustrate the efficiency of the proposed techniques.