Abstract In this paper, the H∞ control problem is investigated for a time-delayed two-dimensional (2-D) network under the random access protocol (RAP). The control input is transmitted to the actuator via a network with communication constraint, where only one signal obtains the network access at each transmission instant, and the RAP is adopted here to schedule the data transmission which is depicted by an independent and identically distributed sequence. The randomly occurring uncertainty, nonlinearity and unknown time delays are all introduced in the underlying 2-D system. The aim of the addressed problem is to design an observer-based controller so that the considered 2-D system has a predefined H∞ performance index. Sufficient condition is given to ensure the H∞ performance of the closed-loop system via the Lyapunov theory and stochastic analysis. Moreover, the observer-based controller is dexterously designed to ensure the achievement of the H∞ performance, under which the controller gains are designed by solving certain matrix inequalities. Finally, a numerical example is given to demonstrate effectiveness of the proposed approach.

中文翻译：

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随机访问协议下二维延迟网络基于观察者的H∞控制

摘要 本文研究了随机访问协议(RAP) 下时滞二维(2-D) 网络的H∞ 控制问题。控制输入​​通过具有通信约束的网络传输到执行器，其中在每个传输时刻只有一个信号获得网络访问，这里采用RAP来调度数据传输，由独立同分布的序列描述。随机发生的不确定性、非线性和未知的时间延迟都在底层二维系统中引入。所解决问题的目的是设计一个基于观测器的控制器，以便所考虑的二维系统具有预定义的 H∞ 性能指标。通过Lyapunov理论和随机分析给出了保证闭环系统H∞性能的充分条件。此外，基于观察器的控制器被巧妙地设计以确保实现 H∞ 性能，在此情况下，控制器增益是通过解决某些矩阵不等式来设计的。最后，给出了一个数值例子来证明所提出方法的有效性。