@incollection{eprints2480,
           title = {Sparse solutions to the average consensus problem via L1-Norm regularization of the fastest mixing Markov-Chain problem},
            year = {2014},
           month = {December},
           pages = {2228--2233},
       booktitle = {Proceedings of the 53rd Annual Conference on Decision and Control (CDC)},
            note = {53rd Annual Conference on Decision and Control (CDC), held in Los Angeles (USA) 15-17 December 2014 },
       publisher = {IEEE},
          author = {Giorgio Gnecco and Rita Morisi and Alberto Bemporad},
        keywords = {Optimization, Sensor networks, Linear systems},
             url = {http://eprints.imtlucca.it/2480/},
        abstract = {In the ?consensus problem? on multi-agent systems, in which the states of the agents are ?opinions?, the agents aim at reaching a common opinion (or ?consensus state?) through local exchange of information. An important design problem is to choose the degree of interconnection of the subsystems so as to achieve a good trade-off between a small number of interconnections and a fast convergence to the consensus state, which is the average of the initial opinions under mild conditions. This paper addresses this problem through l1-norm regularized versions of the well-known fastest mixing Markov-chain problem, which are investigated theoretically. In particular, it is shown that such versions can be interpreted as ?robust? forms of the fastest mixing Markov-chain problem. Theoretical results useful to guide the choice of the regularization parameters are also provided, together with a numerical example.}
}