Multi-Event-Triggered Control with Reduced Packet Sizes for Quantized Discrete-Time Linear Systems

This paper proposes a multi-event-triggering policy with reduced packet sizes for networked and quantized discrete-time linear systems. Unlike conventional event-triggered state feedback control methods in which all the system states must be sent to the controller at any triggering times, the proposed method samples each state based on its dynamical behavior and leads to properly-tuned inter-event intervals. Towards this aim, proceeding by emulation and in the absence of any event-triggered sampling, a state feedback control law is first designed. Then, the obtained closed-loop system is taken into account as a multi-time scale system based on its real Jordan form. Next, even-triggering mechanisms (ETMs) are designed for the Jordan blocks by considering their transient behavior, which result in different sequences of triggering times for the transmission of the states. This makes it possible to manage both the size and number of packets sent to the controller. The ultimate boundedness of the closedloop system with state quantization is proved through precise analysis. To showcase the validity of the theoretical results, a simulation study is conducted where the proposed controller is applied to an inverted pendulum system.