Stabilizing bit rate conditions for a scalar linear event-triggered system with Markov dropouts

This paper investigates the stabilization problem of a scalar linear event-triggered system via a bit-rate-limited network, which suffers from bounded transmission delay and Markov feedback dropouts. Necessary and sufficient bit rate conditions for the asymptotic stability of the concerned system are derived in the mean square sense. Due to the influence of transmission delay and Markov dropouts, a higher bit rate is required for stabilization, which is quantitatively characterized. To overcome the difficulties induced by the temporal correlation of Markov dropouts, a variable bit rate quantization policy is proposed to achieve the minimum-bit-rate stability by appropriately determining the number of quantization bits for each feedback packet. The obtained sufficient bit rate condition is shown to be also necessary in some special cases. Simulations are done to verify the effectiveness of our results.