Synchronisation of stochastic delayed multi-agent systems with uncertain communication links and directed topologies

This study investigates the mean square exponential (MSE) synchronisation problem for the multi-agent systems with multiplicative noises, where the communication topologies among the agents are directed and time varying. The phenomenon of randomly varying coupling delay is considered and described by a Bernoulli distributed white sequence with known probability, thereby better reflecting the practical system dynamics. Network topologies proposed in this study are directed and time varying which intrinsically characterise the random communications between agents. By exploiting the graph theory and the coordinate transformation method, the MSE synchronisation problem for the stochastic multi-agent network is converted into a robust MSE stability problem for the transformed system. Then by constructing a Lyapunov functional and utilising the properties of Kronecker product, both delay-independent and delay-dependent sufficient conditions are derived guaranteeing the transform system to be robustly stable in the mean square. The criteria established are in the form of matrix inequalities which can be solved and checked easily. Finally, simulation examples are provided to illustrate the validity for the obtained results.

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