This article is concerned with the reliable H_∞ control problem against actuator failures for discrete two‐dimensional (2‐D) switched systems with state delays and actuator faults described by the second Fornasini‐Marchesini (FM) state‐space model. By resorting to the average dwell time (ADT) approach, also by constructing an appropriate Lyapunov‐Krasovskii functional and using the Wirtinger inequality, some sufficient conditions for the exponential stability analysis and weighted H_∞ performance of the given system are derived. Then, based on the obtained conditions, a reliable H_∞ controller design approach is presented such that the resulting closed‐loop system is exponentially stable with a weighted H_∞ performance , not only when all actuators are in normal conditions, but also in the case of some actuator failures. Finally, two numerical examples are examined to demonstrate the effectiveness of the proposed results.

中文翻译：

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具有状态延迟和执行器故障的二维离散开关系统的可靠H∞控制

本文涉及的是可靠ħ _∞针对致动器故障的控制问题，用于通过所述第二Fornasini-Marchesini的（FM）状态空间模型描述状态的延迟和致动器的故障离散二维（2-d）切换系统。诉诸的平均停留时间（ADT）的方式，也通过构建一个适当的Lyapunov-Krasovskii泛函和使用该Wirtinger不等式，对于指数稳定性分析和加权的充分条件ħ _∞给定的系统的性能导出。然后，基于所获得的条件下，可靠ħ _∞呈现控制器的设计方法，使得所得闭环系统是指数稳定的与加权ħ_∞性能，不仅在所有执行器都处于正常状态时，而且在某些执行器发生故障时也是如此。最后，研究了两个数值示例，以证明所提出结果的有效性。