Consensusability of discrete-time multi-agent systems under binary encoding with bit errors

Abstract

This paper is concerned with the consensusability problem for a class of discrete-time multi-agent systems (DT-MASs). A binary encoding scheme (BES) is employed during the data transmission, and only a finite-length binary bit string is transmitted due primarily to the limited network bandwidth in practice. Meanwhile, the binary bit string, transmitted via memoryless binary symmetric channels, might suffer from random bit errors with a certain probability. The purpose of this paper is to derive some consensusability conditions, under which there must exist a distributed controller such that the mean-square bounded consensus is achieved by the considered DT-MASs with BESs subject to random bit errors. To this end, the statistical properties are first revealed for the BES-induced quantization errors and the random bit errors. Then, by resorting to the solvability analysis of a modified Riccati inequality, some sufficient conditions are, respectively, derived to ensure the mean-square bounded consensus under the undirected communication topology in two scenarios: (1) identical bit-error rates (BERs); and (2) non-identical BERs. In particular, a necessary and sufficient condition is established for a single input case with identical BERs. Furthermore, the ultimate upper bound of the consensus errors in the mean-square sense is established to examine the effects of the length of bit string and the BERs. Finally, an illustrative simulation example is provided to validate the effectiveness of the theoretical results.