  This paper considers the cluster synchronization problem of generic linear
dynamical systems whose system models are distinct in different clusters. These
nonidentical linear models render control design and coupling conditions highly
correlated if static couplings are used for all individual systems. In this
paper, a dynamic coupling structure, which incorporates a global weighting
factor and a vanishing auxiliary control variable, is proposed for each agent
and is shown to be a feasible solution. Lower bounds on the global and local
weighting factors are derived under the condition that every interaction
subgraph associated with each cluster admits a directed spanning tree. The
spanning tree requirement is further shown to be a necessary condition when the
clusters connect acyclically with each other. Simulations for two applications,
cluster heading alignment of nonidentical ships and cluster phase
synchronization of nonidentical harmonic oscillators, illustrate essential
parts of the derived theoretical results.
