@ARTICLE{aminzare_sontag_synchronization2014,
   AUTHOR       = {Z. Aminzare and E.D. Sontag},
   JOURNAL      = {IEEE Transactions on Network Science and Engineering},
   TITLE        = {Synchronization of diffusively-connected nonlinear 
      systems: results based on contractions with respect to general norms},
   YEAR         = {2014},
   OPTMONTH     = {},
   OPTNOTE      = {},
   NUMBER       = {2},
   PAGES        = {91-106},
   VOLUME       = {1},
   KEYWORDS     = {matrix measures, logarithmic norms, synchronization, 
      consensus, contractions, contractive systems},
   PDF          = {../../FTPDIR/aminzare_sontag_synchronization_ieee_networks2014.pdf},
   ABSTRACT     = {Contraction theory provides an elegant way to analyze 
      the behavior of certain nonlinear dynamical systems. In this paper, 
      we discuss the application of contraction to synchronization of 
      diffusively interconnected components described by nonlinear 
      differential equations. We provide estimates of convergence of the 
      difference in states between components, in the cases of line, 
      complete, and star graphs, and Cartesian products of such graphs. We 
      base our approach on contraction theory, using matrix measures 
      derived from norms that are not induced by inner products. Such norms 
      are the most appropriate in many applications, but proofs cannot rely 
      upon Lyapunov-like linear matrix inequalities, and different 
      techniques, such as the use of the Perron-Frobenious Theorem in the 
      cases of L1 or L-infinity norms, must be introduced.}
}

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