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In this study, the authors study the finite-time cluster synchronisation problem for a class of Markovian switching complex networks with stochastic noise perturbations. By constructing the suitable stochastic Lyapunov-Krasovskii functional, using finite-time stability theorem, inequality techniques and the properties of Weiner process, sufficient conditions are obtained to ensure finite-time cluster synchronisation for the complex networks with or without time delays. The effects of control parameters on cluster synchronisation speed and time delays are also analysed. Since finite-time cluster synchronisation means the optimality in convergence time and has better robustness and disturbance rejection properties, this study has important theory significance and practical application value. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results. NomenclatureThroughout this paper, R n and R n×m denote, respectively, the n-dimensional Euclidean space and the set of all n × m real matrices. The superscript 'T' denotes the transpose and the notation X ≥ Y (respectively, X > Y ) where X and Y are symmetric matrices, means that X − Y is positive semi-definite (respectively, positive definite); I N is the identity matrix with compatible dimension. · refers to the Euclidean vector norm; the notation A ⊗ B stands for the Kronecker product of matrices A and B. If A is a matrix, λ min (·) denotes the minimum eigenvalue. diag {· · · } stands for a block-diagonal matrix. E[x] means the expectation of the random variable x. Matrices, if their dimensions are not explicitly stated, are assumed to be compatible for algebraic operations.

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In this paper, we address the consensus problem of second-order multi-agent system with sampled-data and packet losses. A Bernoulli stochastic variable is used to characterize the random packet losses in second-order multi-agent system with sampled-data information, in which packet losses are modeled in a successive way. Based on the matrix exponential and stochastic analysis techniques, several sufficient conditions are given to ensure the almost surely synchronization of second-order multi-agent networks with sampled-data and packet losses, where the graph among the agents is a directed network containing a directed spanning tree. Additionally, we further investigate the almost surely consensus for such system containing time-delays and packed dropouts. On this occasion, the communication graph among the agents is represented by an undirected connected graph. Furthermore, it is found that the probability of packet losses and the modulus of eigenvalues of the Laplace matrix play a vital role in achieving almost surely consensus. In the end, the developed results are applied to the coordination of multiple vehicles. Two examples are provided to illustrate the effectiveness of our results.INDEX TERMS Consensus analysis, synchronization, packet dropouts, sampled-data, time-delay. YANG TANG (M'11) received the B.S. and Ph.D. degrees in electrical engineering from