Synchronization for linear singularly perturbed complex networks with coupling delays

Abstract

This paper is concerned with the synchronization problem about linear singularly perturbed complex network system with coupling delay. The sufficient delay-dependent conditions for the synchronization of the network are established by introducing an equivalent network system with the Lyapunov stability theory. These conditions, which are formulated in terms of linear matrix inequalities, can be solved efficiently by the LMI toolbox of MATLAB. A simulation example is provided to show the validity of the proposed the synchronization conditions of the whole network.

Decomposition approach to exponential synchronisation for a class of non‐linear singularly perturbed complex networks

“…When the positive constant η is sufficiently small, the condition (31) will guarantee ηP f + P f G + G T P f − cγ P f < 0, soV (Z(τ ))| (14) < 0 holds, that is, the system (14) is asymptotically stable at the original equilibrium point. Since the fast sub-network (14) is linear, its asymptotical stability is equivalent to the exponential stability, both of which are global behaviours.…”

“…Summarising the discussions made so far, there is a practical need to introduce a new type of complex networks with singular perturbations. In [31], some pioneering work has been reported to show the importance of studying the synchronisation problem for the angle velocity of rotor mechanics of an electric power network with N synchronous machines. Note that the smart grids, which include the electric power networks as a special case, are a typical kind of SPCN.…”

Bounded synchronisation of singularly perturbed complex network with an application to power systems

“…Thus, it is important to study the synchronisation of singularly perturbed complex networks. To the best of our knowledge, however, little attention has been paid to the synchronisation of singularly perturbed complex networks [16].…”