Mixed analog–digital method of designing a heterogeneous network with the desired collective behavior and rapid convergence

Among many advances given by the diffusive coupling on the synchronization problem, recently a design method for a continuous-time heterogeneous network with the desired collective behavior has been developed. Meanwhile, by its use of high-gain, implementation issues arise in discrete-time frameworks. The goal of this paper is thus to introduce a simple scheme that follows the philosophy of Carver Mead, a pioneer of VLSI (Very Large Scale Integration) technology, that removes those implementation issues. In the end, we utilize what corresponds to derivative consensus in continuous-time, which can be realized by, for instance, an analog electric circuit. This provides a mixed analog–digital method of designing a heterogeneous network with the desired collective behavior and rapid convergence.