Quantized stabilization of event-triggered systems under independent and identical distributed packet dropouts

This article studies the quantized control problem of a scalar continuous-time linear system over a digital network. The network is subject to bounded transmission delay and independent and identically distributed packet dropouts. Event-triggered sampling is implemented in the system. We first derive a lower bound on the necessary bit rate for any event-triggered strategy by analyzing the evolution of the uncertainty set of the system state. Then we propose a control strategy which combines both event-triggering and time-triggering to stabilize the system. Note that our control strategy implements a dynamic encoding policy, under which the number of quantization bits is dependent on dropouts. Although the average bit rate occupied by our control strategy is higher than the obtained lower stabilizing bit rate bound, their gap can arbitrarily approach zero by relaxing the integer requirement of the number of quantization bits. Numerical examples are given to illustrate the derived results.

Automated summary

This article studies the quantized control problem of a scalar continuous-time linear system over a digital network. By analyzing the evolution of the uncertainty set of the system state, a lower bound on the necessary bit rate for any event-triggered strategy is derived, and a control strategy combining event-triggering and time-triggering is proposed to stabilize the system. Numerical examples are provided to illustrate the obtained results.