  This paper studies the consensusability problem of multi-agent systems
(MASs), where agents communicate with each other through Markovian packet loss
channels. We try to determine conditions under which there exists a linear
distributed consensus controller such that the MAS can achieve mean square
consensus. We first provide a necessary and sufficient consensus condition for
MASs with single input and i.i.d.\ channel losses, which complements existing
results. Then we proceed to study the case with identical Markovian packet
losses. A necessary and sufficient consensus condition is firstly derived based
on the stability of Markov jump linear systems. Then a numerically verifiable
consensus criterion in terms of the feasibility of linear matrix inequalities
(LMIs) is proposed. Furthermore, analytic sufficient conditions and necessary
conditions for mean square consensusability are provided for general MASs. The
case with nonidentical packet loss is studied subsequently. The necessary and
sufficient consensus condition and a sufficient consensus condition in terms of
LMIs are proposed. In the end, numerical simulations are conducted to verify
the derived results.
