Sufficient bit rate conditions to stabilize an uncertain scalar nonlinear system based on event triggering

Abstract

This paper considers to stabilize an uncertain scalar continuous-time nonlinear system with bounded network delay and process noise, which transmits all feedback signals through a digital communication network. In order to save the bandwidth of the feedback network, stability is expected to be maintained at as low as possible feedback bit rate. Based on event triggering, this paper proposes a model-based event-triggered sampling strategy to guarantee the desired input-to-state stability of the concerned system. Due to the bounded network delay, the receiving time instant of a feedback packet cannot be precisely controlled by the sensor, i.e., the receiving time instant is not always equal to its sampling time instant. Their gap, i.e., the network delay, determines how much information can be carried through the receiving time instant and makes great impact on the system’s stability. Sufficient bit rate conditions to stabilize that system are derived. The conditions are determined by the parameter of Lipschitz condition, the upper bound of the network delay and the system uncertainty. Compared with the periodic sampling strategies, a lower bit rate is required by the proposed event-triggered strategy. Simulations are done to verify the effectiveness of the achieved stabilizing bit rate conditions.