Sufficient stabilizing bit rate conditions for an n-dimensional nonlinear system based on event triggering

Abstract

This paper investigates the problem of stabilizing an n-dimensional nonlinear system whose feedback packets are transmitted via the digital network. In the presence of the bounded processing delay and network delay, the sampling time instant of a feedback packet is not the same as its receiving time instant. The larger difference between these time instants, the higher bit rate is required to stabilize the concerned system. Moreover, not only these delays, but also feedback dropouts and process noise will deteriorate the system performance. Thus we propose a model-based event-triggered control method to stabilize the system and save the occupied network bandwidth. Besides the transmission bits inside the feedback packets, their sampling time instants also convey the state information. The proposed event-triggered method can make full use of the feedback packets, especially their receiving time instant information. Compared with the periodic sampling method, our method performs better and requires lower stabilizing bit rates while the desired input-to-state stability can still be ensured. The obtained bit rate conditions only depend on the Lipschitz constant, the upper bounds of the delays and the dropout rate, and are independent of the bounded process noise.

Keywords: Feedback dropouts; Model-based event-triggered control; Nonlinear system; Stabilizing bit rate conditions.