In this paper, the H ∞ control problem for a class of two-dimensional (2-D) linear discrete-time systems with fading measurements is investigated, where the 2-D systems are described by a Roesser model. The Rice fading model is applied to describe the fading phenomenon and the coefficients of the model satisfy the independent identical Gaussian distributions. The main objective of this paper is to design a controller such that both the 2-D closed-loop system is exponentially mean-square stable and the prescribed H ∞ performance is guaranteed under the condition of applying the attenuation signals. By utilizing the Lyapunov stability theory and the linear matrix inequalities (LMIs) techniques, sufficient conditions are conducted to guarantee the desired tracking performance. Based on such conditions, the gain matrix of the proposed controller is obtained. Finally, the effectiveness of the proposed control schemes is illustrated with a numerical example and a Darboux equation example.

中文翻译：

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一类具有衰落测量的二维线性系统的H∞控制

在本文中，研究了一类具有衰落测量的二维 (2-D) 线性离散时间系统的 H ∞ 控制问题，其中二维系统由 Roesser 模型描述。应用Rice衰落模型来描述衰落现象，该模型的系数满足独立的相同高斯分布。本文的主要目标是设计一个控制器，使得在施加衰减信号的条件下，二维闭环系统是指数均方稳定的，并且保证规定的 H ∞ 性能。通过利用李雅普诺夫稳定性理论和线性矩阵不等式 (LMI) 技术，有足够的条件来保证所需的跟踪性能。基于这样的条件，获得了所提出的控制器的增益矩阵。最后，通过数值例子和 Darboux 方程例子说明了所提出的控制方案的有效性。