Event-Triggered Stabilizing Bit Rate Conditions for an n-Dimensional Linear System With i.i.d. Feedback Dropouts.

Abstract

This article aims to stabilize an n -dimensional linear time-invariant (LTI) system, whose feedback packets are transmitted through a digital communication network. The digital network suffers from network delay and independent and identically distributed (i.i.d.) feedback dropouts, which may destabilize the system. The coupling among multiple state variables may further harm the stability of the system. In order to deal with these issues and save the occupied bandwidth of the feedback network, we propose a periodic event-triggering strategy. In our strategy, the state is measured periodically, but only quantized and transmitted when a certain condition is triggered. By well balancing the state coupling and making full use of both the information inside transmitted feedback packets and the one carried by sampling time instants, our strategy can maintain the desired mean square stability at a lower bit rate than conventional periodic sampling policies. The obtained stabilizing bit rate conditions are determined by the processing and network delays, the dropout rate, and the unstable eigenvalues of the system matrix, but independent of the process noise. Moreover, the lack of the direct state access does not incur any additional stabilizing bit rate. Simulations are done to confirm the effectiveness of the obtained stabilizing bit rate conditions.