Event-Triggered Control for Linear Positive Discrete-Time Singular Systems With Time Delay

This study addresses the stabilization of discrete-time singular systems with delays by employing an event-triggered control (ETC) method. In particular, we propose an innovative triggering mechanism that compares the measurement-error coordinates with the system state coordinates, thereby preserving system positivity even under time delays. A novel algorithm is introduced, which relies on comparing the coordinates of measurement errors and system states to maintain the positivity of the system. This article establishes sufficient conditions to ensure that the closed-loop system remains regular, causal, positive, and exponentially stable, building upon this newly formulated triggering approach and leveraging advanced matrix properties such as nonnegative matrices. To illustrate the efficacy and nontrivial nature of these conditions, we provide an algorithmic diagram and a diverse set of examples, including both simulations and a practical case study. The ETC mechanism, characterized by the sequence of event occurrences, demonstrates substantial nontrivial properties. These conditions are easily verifiable using MATLAB tools. This article also includes a range of examples, featuring both numerical simulations and a practical case study, to validate the effectiveness of the theoretical findings.