The admissible consensus problem of singular multi-agent systems (SMASs) with mismatched norm-bounded parametric uncertainties and unknown norm-bounded disturbances is investigated by an integral sliding mode technique. Under a directed spanning tree network of the state transmission graph, the error states are defined. Then a linear matrix inequality (LMI)-based sufficient condition is presented to guarantee regularity, free impulse, quadratic stability and H_∞ performance of the sliding mode dynamics of the error states. Next, an integral sliding manifold parameter is designed to decrease the order of the LMI caused by the parametric uncertainties, and matrix inversion formulas and inequality techniques are applied to reduce the conservativeness of the LMI. Finally, the control laws, relying on the error states, the property of the state transmission graph and the upper norm bound of disturbances, are presented to ensure the state trajectories of the resulting closed-loop system to achieve robust admissible consensus with H_∞ performance. A simulation example is provided to show the effectiveness of the proposed method.

中文翻译：

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使用滑模方法的奇异多智能体系统的鲁棒可容许共识

通过积分滑模技术研究了具有不匹配范数有界参数不确定性和未知范数界扰动的奇异多智能体系统 (SMAS) 的可容许一致性问题。在状态传输图的有向生成树网络下，定义了错误状态。然后提出了一个基于线性矩阵不等式 (LMI) 的充分条件来保证正则性、自由脉冲、二次稳定性和H _∞错误状态的滑模动力学性能。接下来，设计了一个积分滑动流形参数来降低由参数不确定性引起的LMI的阶数，并应用矩阵求逆公式和不等式技术来降低LMI的保守性。最后，根据误差状态、状态传输图的性质和扰动的上限范数，提出控制律，以确保所得闭环系统的状态轨迹，以实现具有H _∞性能的鲁棒可容许一致性. 提供了一个仿真例子来证明所提出方法的有效性。