LMI-based criteria for synchronization of complex dynamical networks

This paper considers the problem of controlling a complex dynamical network by means of pinning. We point out that the synchronization criterion given in the form of matrix eigenvalues can be equivalent to a linear matrix inequality criterion. We further investigate network synchronization via pinning and prove several linear matrix inequality theorems. In particular, we theoretically provide two typical pinning strategies based on whether the graph which is made up of unpinned nodes and edges between them is irreducible or not. Numerical simulations including k-regular networks, star-shaped networks and BA scale-free networks, are shown for illustration and verification.