Event-triggered control of positive switched systems based on linear programming

Abstract

This study focuses on the problem of event-triggered control for positive switched systems without/with input saturation in both continuous-time and discrete-time contexts. First, a 1-norm based event-triggering mechanism is established for continuous-time positive switched systems. By means of the matrix decomposition technique, an event-triggered controller for the systems is designed by decomposing controller gain matrix into non-positive and non-negative components. Under the designed controller, the resulting closed-loop systems are positive and stable. For the systems with input saturation, the saturation term is transformed into interval form under the event-triggering condition. Then, an event-triggered controller gain matrix and a cone domain of attraction gain matrix are designed for the corresponding interval systems in terms of linear programming, respectively. Furthermore, the presented approaches are extend to discrete-time positive switched systems without/with input saturation. Compared with existing results on positive switched systems, the designed event-triggered controller can reduce sampling frequency and save resources. Finally, two numerical examples are provided to verify the effectiveness of the obtained results.