Event-Triggered Control of Delayed Linear Systems Using Linear Programming

This letter presents a novel coordinate-wise event-triggered control mechanism for stabilizing and ensuring positivity of continuous-time linear systems with time delay. By explicitly comparing each state coordinate against individual thresholds, we achieve a more accurate determination of when the event-triggered condition is violated. This approach ensures positivity, since each coordinate is treated independently within the triggering condition, and effectively handles the destabilizing influence of delay. We formulate the stability and positivity criteria as solvable linear programming constraints. Additionally, we prove that the proposed mechanism excludes Zeno behavior by guaranteeing a positive lower bound on inter-event times. Numerical examples illustrate that our method balances system performance and reduced triggering frequency far more effectively than time-triggered strategies.