Controlled synchronization via nonlinear integral coupling

This paper considers the problems of controlled synchronization and regulation of oscillatory systems. For a specific class of nonlinear systems, namely for minimum phase systems with relative degree one, we propose a systematic design procedure for finding nonlinear couplings between the systems - both unidirectional and bidirectional - that guarantee asymptotic synchronization of the systems' states for arbitrary initial conditions. The corresponding coupling has the form of an integral and it can be considered as a generalized distance between the outputs of the coupled systems. It combines both the low- and the high-gain coupling design in one nonlinear function. The results are illustrated with simulations of coupled Hindmarsh-Rose neuron oscillators.