Model reduction of linear multi-agent systems by clustering with H-2 and H _ infinity error

In the recent paper (Monshizadeh et al. in IEEE Trans Control Netw Syst 1(2):145–154, 2014. https://doi.org/10.1109/TCNS.2014.2311883), model reduction of leader–follower multi-agent networks by clustering was studied. For such multiagent networks, a reduced order network is obtained by partitioning the set of nodes in the graph into disjoint sets, called clusters, and associating with each cluster a single, new, node in a reduced network graph. In Monshizadeh et al. (2014), this method was studied for the special case that the agents have single integrator dynamics. For a special class of graph partitions, called almost equitable partitions, an explicit formula was derived for the H2 model reduction error. In the present paper, we will extend and generalize the results from Monshizadeh et al. (2014) in a number of directions. This research is supported by a research grant of the “International Max Planck Research School (IMPRS) for Advanced Methods in Process and System Engineering (Magdeburg)”. B Petar Mlinarić mlinaric@mpi-magdeburg.mpg.de Hidde-Jan Jongsma h.jongsma@rug.nl Sara Grundel grundel@mpi-magdeburg.mpg.de Peter Benner benner@mpi-magdeburg.mpg.de Harry L. Trentelman h.l.trentelman@rug.nl 1 Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, Groningen, The Netherlands 2 Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany