IEEE Trans Cybern. 2016 Sep;46(9):2132-43. doi: 10.1109/TCYB.2015.2466115. Epub 2015 Aug 25.
This paper is concerned with the consensus of multiagent systems with nonlinear dynamics through the use of aperiodic sampled-data controllers, which are more flexible than classical periodic sampled-data controllers. By input delay approach, the resulting sampled-data system is reformulated as a continuous system with time-varying delay in the control input. A continuous Lyapunov functional, which captures the information on sampling pattern, together with the free-weighting matrix method, is then used to establish a sufficient condition for consensusability. For a more general case that the sampled-data controllers are subject to constant input delays, a novel discontinuous Lyapunov functional is introduced on the basis of the vector extension of Wirtinger's inequality. This functional can lead to simplified and efficient stability conditions for computation and optimization. Further results on the estimate of maximal allowable sampling interval upper bound is given as well. Numerical example is provided to show the effectiveness and merits of the proposed protocol.
本文通过使用非周期性采样控制器来研究具有非线性动力学的多智能体系统的一致性，而非周期性采样控制器比经典的周期性采样控制器更加灵活。通过输入时滞方法，所得到的采样数据系统被重新表述为具有时变控制输入时滞的连续系统。然后，使用连续 Lyapunov 泛函（它捕获了关于采样模式的信息）和自由加权矩阵方法，建立了一致性的充分条件。对于采样控制器受到常数输入时滞的更一般情况，基于 Wirtinger 不等式的向量扩展，引入了一种新的不连续 Lyapunov 泛函。该泛函可以为计算和优化提供简化和高效的稳定性条件。还给出了最大允许采样间隔上界的估计的进一步结果。提供了一个数值示例以显示所提出协议的有效性和优点。
