Global Pinning Controllability of Complex Networks

In this paper, we study pinning-controllability of networks of coupled dynamical systems. In particular, we study the problem of asymptotically driving a network of coupled identical oscillators onto some desired common reference trajectory by actively controlling only a limited subset of the whole network. The reference trajectory is generated by an exogenous independent oscillator, and pinned nodes are coupled to it through a linear state feedback. We describe the time evolution of the complex dynamical system in terms of the error dynamics. Thereby, we reformulate the pinning-controllability problem as a global asymptotic stability problem. Using Lyapunov-stability theory and algebraic graph theory, we establish tractable sufficient conditions for global pinning-controllability in terms of the network topology, the oscillator dynamics, and the linear state feedback.