Periodic Event-Triggered Quantization Policy Design for a Scalar LTI System With i.i.d. Feedback Dropouts

Abstract

This technical note proposes an event-triggered quantization policy design method to stabilize a scalar continuous-time linear time-invariant (LTI) system, whose feedback loop is closed over an unreliable digital communication network. The feedback packets suffer from network delay and may be dropped in an independent and identically distributed (i.i.d.) way. In order to save quantization bit rate, we implement a periodic event-triggering strategy which periodically samples the state and only quantizes and transmits the sampled state when a predefined event is triggered. By making good use of both the information bits and the sampling time instants of the feedback packets, our policy can obtain the desired mean-square stability at a lower bit rate than the conventional time-triggered quantization policies which utilize only the information bits inside the feedback packets. Under our quantization policy, the stabilizing bit rate condition is up to the dropout rate, the processing and network delays and the unstable eigenvalue of the system, and is independent of the bounded process noise.