Data-Driven Event-Triggering Control of Discrete Time-Delay Systems

This paper investigates the data-driven event-triggering control of discrete time-delay systems. When there is enough data available, the system parameters can be determined by identified methods, and the model-based controller design can be implemented. However, with little data, this method does not result in an accurate system. The data-driven control method is introduced to address this issue. This paper classifies discrete-time systems with time delays into those with known delays and those with unknown delays. Controllers for systems with known delays and unknown delays are designed based on limited data, and stability is ensured by constructing improved Lyapunov functions. Two analyses are introduced: For the known delay condition, the lifting model method is presented to raise order and change the time-delay system to a delay-free system. Further, the stabilization criterion is presented. For the unknown time-delay system, according to the basic data-driven assumption, the data-driven stabilization criterion is presented. Also, the introduction of a dynamic event-triggering scheme and the discussion in this paper on how its parameters can be chosen can save more computational resources. Based on the two methods, the Lyapunov function is constructed separately, and the controller is derived through Linear Matrix Inequality. Finally, a discrete time-delay system is used as an example to show the effectiveness of these two methods. In addition, the dynamic event-triggering scheme proposed in this paper is compared with other articles to show that the parameter selection method proposed in this paper has better performance.