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Necessary and Sufficient Bit Rate Conditions to Stabilize a Scalar Continuous-Time LTI System Based on Event Triggering

This paper considers a scalar continuous-time linear time-invariant system, whose feedback signal is transmitted through a communication network. Such a network has only finite bit rate and suffers from transmission delay which is characterized by both lower and upper delay bounds. The concerned system implements event-triggering strategies, i.e., only when certain events are triggered, the system samples and transmits feedback signals. This paper first derives some lower bounds on the feedback bit rate required to achieve the input-to-state stability under arbitrary event-triggering strategies. Then this paper proposes some constructive methods to design the event-triggering strategy and the controller, and can achieve the input-to-state stability at a bit rate being arbitrarily close to these obtained lower bit rate bounds. Moreover, this paper proves that the stabilizing bit rates under the proposed event-triggering strategies can be strictly lower than the stabilizing bit rate required by any time-triggering strategy. This bit rate superiority comes from the fact that under event triggering, the state information can be freely extracted from the receive time instants of feedback packets without consuming any bit rate. Simulations are done to demonstrate the bit rate superiority of the proposed event-triggering strategies.