Contraction-based internal model design and application to output synchronization

This paper considers a nonlinear internal model design based on the contraction theory (or simply contraction). A sufficient condition is presented for constructing a class of internal models enjoying certain input-to-state stability. The method is further applied to solve an output synchronization problem of a class of second-order leader-follower multi-agent systems. An example of synchronizing a group of mass-spring systems with a Rayleigh oscillator is given for an illustration.