A Decentralized Event-Triggered State-Feedback Control Technique for Continuous-Time Linear Systems

In this article, a decentralized event-triggered technique is developed to effectively implement the state-feedback controllers for a class of linear systems. Toward this end, the system dynamics is represented in its Jordan canonical form, and the system states are sorted based on their time constants. Then, for any Jordan block, an event-triggered mechanism is designed to determine the execution times for sampling and sending its corresponding state variable(s) to the controller. In this way, each Jordan block has a mechanism to decide whether or not its data should be transmitted to the controller. Using the proposed technique, event-triggered policies can be designed such that the fast dynamics are sampled with short interevent intervals, while the slower dynamics are simultaneously permitted to send their data with relatively long interevent intervals. The proposed technique decreases both the number and the size of transmitted packets. The boundedness of the closed-loop system is guaranteed under the suggested event-triggered technique. Moreover, it is proved that the Zeno behavior is avoided. In comparison with ordinary event-triggered methods, the proposed decentralized event-triggered technique leads to better performance due to its extra degrees of freedom in sending the data from the system to the controller. Numerical simulations are presented to illustrate the promising features of the suggested event-triggered controller.