Dynamic consensus of multi-agent systems under Markov packet losses with defective transition probabilities

This paper is concerned with the consensus problem of discrete-time multi-agent systems (MASs) over lossy communication channels. The communication connection between agents at initial time is assumed to be accessible, which ensures that the system can reach consensus over ideal communication channels. However, the communication channel can be fading in practice, packet loss occurs inevitably. In this paper by modeling the packet losses as a Markov process with defective transition probabilities, a new description of the scenario of packet losses is addressed. Since the transition probabilities considered here comprise three types: known, uncertain within given intervals, and unknown, our model is more general and practical than previous results. A distributed protocol is introduced to achieve dynamic consensus. Sufficient condition for the mean-square consensus of discrete-time MASs is derived in the form of linear matrix inequalities. Numerical example is also given to illustrate the effectiveness of the theoretical results.