Dual‐Threshold Event‐Triggered Control for Positive Linear Systems

Abstract

ABSTRACT This paper investigates event‐triggered stabilization for positive linear systems. First, we propose a novel dual‐threshold event‐triggered scheme (ETS) that takes full advantage of the systems' positivity without relying on norm calculations. This scheme dynamically adapts to the varying triggering demands arising from different trends in the state evolution, ensuring prompt and reliable response across all operating conditions. Second, sufficient conditions for the positivity and asymptotic stability of continuous‐time positive systems and discrete‐time positive systems (both with and without time delay) under this scheme are derived separately, and based on these conditions, the corresponding event‐triggered controller is designed. To suppress Zeno behavior in continuous‐time systems, a positive lower bound on the inter‐execution time (IET) is imposed, which guarantees finite event‐triggering density via dwell‐time constraints. Finally, the effectiveness of the proposed framework is validated through two practical applications: a continuous‐time battery management system (for continuous‐time system verification) and a discrete‐time data network transmission model (for discrete‐time system validation with and without time delay).