Networks of discontinuous and nonidentical systems

This line of research aims at removing two simplifying assumption often considered in the study of complex networks: nodes’ dynamics described by i) identical and ii) continuous vector fields. These assumptions do not hold, for instance, in biochemical or power networks, where there are unavoidable parameter mismatches, while in mechanical oscillators with friction and in switching electrical devices it is not realistic to assume nodes’ dynamics continuous and differentiable. Conditions for bounded synchronization were obtained using set-valued Lyapunov functions. Next, self-tuning proportional integral strategies have been devised to achieve complete synchronization in networks nonidentical linear systems. Preliminary experiments on control of network of nonidentical and nondifferentiable systems have been performed on networks of coupled Chua's circuits.