Synchronization of Multi-Agent Hybrid Systems With Synchronous State-Dependent Jumps

In this letter, we investigate the problem of synchronization of multi-agent systems described by hybrid non-linear input affine dynamics. We consider networks described by undirected connected graphs without leader. We present a set of sufficient conditions based on an LMI approach in order to design a state-feedback distributed control law. Then, by exploiting the properties of the graph incidence matrix we provide an optimization of the tuning parameters. The incidence matrix properties also allow us to construct a Lyapunov function to establish synchronization of the hybrid network.