Synchronization via Pinning Control on General Complex Networks

By Wenwu Yu, Guanrong Chen, Jinhu Lu, Jürgen Kurths. SIAM Journal of Control and Optimization, 2013

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Control Principles of Complex Networks (2015, background): “If h(x) = Γx and the oscillator dynamics f(x) satisfies (x− y)T[f(x, t)− f(y, t)] ≤ (x− y)TKΓ(x− y) (105) for a constant matrix K, sufficient conditions for global pinning synchronizability can also be derived (Song and Cao, 2010; Yu et al., 2013, 2009b).”
Synchronization Control for A Class of Discrete Time-Delay Complex Dynamical Networks: A Dynamic Event-Triggered Approach (2019, background): “For those complex networks where the state of each node evolves asynchronously, a variety of effective synchronization control schemes have been proposed, such as pinning control [10], [20], [21], [36], impulsive control [7], [37], and sampled-data control [13], [17].”
Finite-time synchronization of complex delayed networks via intermittent control with multiple switched periods (2016, methodology): “Until now, in order to treat the synchronization problem for a complex network, some control schemes such as state observer-based control [12], impulsive control [13–15], adaptive control [16,17,19], pinning control [5,6,8], sliding mode control [20], projective synchronization scheme [21–23] and in”