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Consensus analysis and design problem for discrete-time linear multi-agent systems (DLMAS) under directed information topology is investigated. A proper linear transformation is proposed to transform the consensus problem to the partial stability problem of a corresponding linear system. Then, a new consensus criterion in terms of Schur stability of matrices for DLMAS achieving consensus under directed information topologies and a state consensus function in analytical formulae are given. Moreover, a design process to determine the feedback gain matrix in the consensus protocol is proposed. Numerical examples are given to validate the above theoretical results.
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