Incremental-dissipativity-based synchronization of interconnected systems

In this paper, the incremental-dissipativity is used to investigate synchronization of a class of dynamical networks from an input-output point of view. The network consists of subsystems described by input-output operators. Firstly, the concept of incremental-passivity is extended to incremental-dissipativity, and it shows that the incremental-dissipativity of the subsystems leads to the dissipativity of a group of virtual systems each of which is related to an individual subsystem. Then the synchronization problem is transformed into the stability problem of a system interconnected by the virtual systems. By utilizing the stability theory of large-scale systems, a sufficient condition is obtained which ensures the input-output synchronization of the network. The counterparts of the main result and the discussion on conditions of the incremental-dissipativity for the subsystems with state space representations are also presented. Finally, an example is given to show the effectiveness of the proposed result.