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This paper first studiesasynchronous synchronisation control problem for Markovian coupled neural networks with missing information. As information exchanges among neural networks, which can help achieving synchronisation, are conducted via a generally unprotected communication network with limited bandwidth, nodes' state information and the synchronised state information may not be available to node  i , and a Bernoulli process is used to model this phenomenon. Furthermore, considering that the amount of information needs to be transmitted is decided by the coupling relationship, missing information rate is assumed to be node- and coupling dependent. By introducing another nonhomogeneous Markov chain with transition probability matrix depending on coupling mode, the asynchronous synchronisation controller is designed, which can describe complex asynchronous switch phenomenon between system and controller modes and covers mode-dependent controller and mode-independent one as two special cases. Three sufficient conditions respectively guaranteeing the global synchronisation and theglobal synchronisation of the addressed networks are obtained, and then the asynchronous synchronisation controller design method is proposed. Finally, an illustrative example with results demonstrating the effectiveness of the given controller design approach is provided.

H ∞ asynchronous synchronisation control for Markovian coupled delayed neural networks with missing information