Event‐triggered feedback stabilisation of switched linear systems under finite bit rates

Abstract

This study considers to asymptotically stabilise a switched linear system which transmits its feedback signals through a digital communication network. Such network can only provide a finite bit rate to represent feedback signals. In the concerned switched linear system, the mode mismatch may occur between the sensor and the controller due to the unknown switching time instants. It assumes that the mode switching is slow enough in the sense of combined dwell time and average dwell time, each individual mode is stabilisable and the available feedback bit rate is high enough, but still finite. In order to save network bandwidth resources, novel event-triggering strategies are implemented, i.e. only when pre-defined events are triggered, the system samples and transmits feedback signals. Then under the proposed event-triggering strategies, a stabilising bit rate condition for the concerned switched linear system is derived. Moreover, this study proves that the obtained stabilising bit rate under the proposed event-triggering strategies can be strictly lower than the stabilising bit rate required by the earlier work based on periodic sampling. Simulations are done to illustrate the bit rate superiority of the proposed event-triggering strategies.