Stabilizing bit rate conditions for a scalar continuous time linear system with bounded processing delay and bounded process noise

Abstract

This paper considers the input-to-state stability of a scalar continuous-time linear control system whose feedback information is transmitted through digital communication networks. It shows that when a packet is transmitted, not only the bits inside that packet but also the transmission time instant of that packet carries information. Scheduling transmission time instants of packets can be viewed as a type of temporal quantization of sampling time instants and effectively transmit state information. Due to processing delay, there is unavoidable non-zero difference between the sampling time instant of a packet and its corresponding transmission time instant, which is called “timing error” and determines the amount of information carried by this temporal quantization. By quantitatively analyzing the effects of timing error on the input-to-state stability of the concerned system, this paper provides some stabilizing bit rate conditions. These conditions are only up to the system matrix and the timing error, and are free of bounded process noise. Through event-triggering schemes, we realize these conditions which may require much lower bit rates to stabilize a scalar continuous-time linear system than the periodic sampling schemes. Simulations confirm the effectiveness of the obtained bit rate conditions.