Bit rate conditions to stabilise a scalar linear system with measurement noise based on event triggering

This paper investigates the input-to-state stability (ISS) problem for a scalar continuous-time linear system with measurement noise under event-triggered sampling. The feedback information is transmitted through a digital communication network with bounded delay. Due to measurement noise, it is difficult to perfectly capture the system's state, which may harm the performance, and even destabilise the system. In order to deal with the measurement noise, a state observer is incorporated into the event generator. By designing the event-triggering strategy based on the observed state, the input-to-state stability of the concerned system can be ensured. We quantitatively analyse the required stabilising bit rate, which is mainly determined by the network delay and the system's dynamics. By selecting appropriate parameters of the event-triggered sampling strategy, the required stabilising bit rate is lower than the one by the conventional periodic sampling strategies. Due to the existence of measurement noise, extra bit rate is required compared with the case with perfect state. The bit rate increase of measurement noise can be arbitrarily reduced at the cost of the degraded control performance, which is measured by the ultimate upper bounds on the state. Simulations are done to illustrate the obtained stabilising bit rate conditions