Pinning Control of MLW-based Complex Dynamical Networks - Discrete Time Case

A new complex dynamical network based on multi-local-world (MLW) model is first introduced. Then, control of this kind of complex dynamical network by applying local feedback injections to a tiny fraction of local worlds in the whole network is investigated. Stability conditions are derived for several different dynamical network models including time-invariant networks, time-varying networks and time-delay networks in discrete-time domain respectively. Especially, stabilization of such networks is completely determined by the coupling strength, the inner-coupling matrix, and by the eigenvalues of the coupling configuration matrix and feedback gain matrix