Pinning Control of Higher Order Nonlinear Network Systems

In this letter, we study the problem of controlling via pinning the motion of nonlinear network systems of any order whose dynamics are in controllable canonical form. Different from existing works that either focus on spontaneous synchronization, assume linear dynamics or rely on dynamics cancellation, here we provide a constructive method to prove pinning controllability towards the desired trajectory selected by the pinner. We introduce an algorithmic procedure that associates to any connected topology a suitable Lyapunov function for the network system. The approach is demonstrated on an illustrative example.