Output group synchronization for networks of heterogeneous linear systems under internal model principle

In this paper, we aim to investigate the output group synchronization problem for a network of heterogeneous linear systems such that the outputs of the nodes, each representing a linear system, synchronize with each other in every cluster. Two different setups in terms of availability of the states of the reference generators are taken into consideration. A unified approach inspired by the internal model principle is proposed. First, the coupled reference generators are constructed so as to produce synchronized reference trajectories. Second, feedback controllers are designed to steer the output of each node to its corresponding reference trajectory. The two setups differ from each other in that the coupling configuration for reference generators and design of feedback controllers are rather different. Specifically, when the states of the reference generators are not available, the small gain theorem is exploited to drive the outputs of the nodes to the synchronized ones of virtual reference generators. Finally, simulations are carried out to validate the theoretical findings.