Event-triggered control for output regulation of discrete-time systems

This paper focuses on the design of event-triggered control mechanisms to achieve output regulation for discrete-time linear systems. It considers an observer-based state feedback controller and proposes conditions to design an event-triggered mechanism that maintains exact regulation while reducing control updates during the transient response. Since for periodic references the event-triggered policy degenerates into a time-triggered policy in steady state, that is, events are generated at each time instant, a relaxed triggering criterion is proposed. This mechanism leads to a practical output regulation with an acceptable error bound. For both the exact and practical cases, conditions in the form of linear matrix inequalities are derived to design the trigger mechanism parameters guaranteeing the closed-loop stability. Optimization problems are therefore proposed to tune these parameters to balance the control updating reduction and the tolerance for output regulation errors in steady state. A numerical example is provided to illustrate the methodology.