An Event-Triggered Adaptive Quantized Feedback Control for LTI Systems

This study's topic is stabilizing a linear time-invariant plant subjected to bounded disturbance using quantized state feedback. We propose an adaptive quantization scheme consisting of two terms, a natural decay term, and a positive coupling proportional to the norm of the state. The proposed procedure ensures the utilization of a lower quantizer resolution if the system is steered away from the origin due to disturbances. In conjunction with dynamic quantization, the event-triggered approach is motivated by the need to utilize computing resources efficiently. The proposed control law and dynamic quantization ensure the system is input-to-state stable (ISS). We ensure that Zeno's phenomenon is absent by showing that the inter-event times are lower bound. We compare the average number of bits the controller requires between the proposed reactive control law and a controller with constant quantization error on a numerical example.