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Bit Rate Conditions to Asynchronously Stabilize Event-triggered Multi-dimensional Linear Systems

Yufei Niu and Qiang Ling*
International Journal of Control, Automation, and Systems, vol. 20, no. 7, pp.2107-2119, 2022

Abstract : "This paper focuses on bit rate conditions to asynchronously stabilize a multi-dimensional linear system based on event triggering. This system transmits control signals through digital communication networks that suffer from processing delay and network delay. So the event-triggering time instants cannot be perfectly known by the controller, which results in the asynchronous state estimation at the sensor and controller sides. To resolve this issue, under the assumption of bounded processing delay and bounded network delay, we propose an event-triggered control strategy to ensure the input-to-state stability for the system. It should be emphasized that this paper does not need to transmit any ACK (Acknowledgment) regarding the receipt of a feedback packet and no clock synchronization is required between the sensor and the controller. Besides the processing delay and the network delay, the coupling among multiple state variables of the multi-dimensional system greatly complicates the event-triggering strategy design and the stability analysis. So we require that the sensor/event-trigger sends the feedback information of each state variable independently and introduce an invertible matrix to simplify the stability analysis. By extracting additional information embedded in the receive time instants of feedback packets, we may obtain a lower bit rate to stabilize the system in the input-to-state sense than periodic sampling methods. The bit rate superiority of our event-triggering strategy is further verified through simulations. "

Keyword : "Event-triggering, input-to-state stability (ISS), multi-dimensional systems, stabilizing bit-rate condition. "

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