This paper investigates the issue of fault-tolerant and anti-disturbance attenuation for a two-dimensional modified repetitive control system (2D MRCS) which is described by switched fuzzy systems with multiple disturbances. In particular, the multiple disturbances contain an exogenous disturbance and standard Wiener noise. Specifically, a generalized extended state observer (GESO) is incorporated with the 2D MRCS to estimate both fault and exogenous multiple disturbances so that the disturbances and faults can be attenuated in the control input. Further, the improved 2D MRCS relaxes the stability condition and provides an enhanced tracking performance. Based on the Lyapunov function approach, pole placement technique and average dwell time approach, the stability criteria for the considered system is developed in terms of linear matrix inequality (LMI). Then an algorithm for designing a GESO-based 2D MRC design is developed based on the obtained LMIs. Further, the results developed are validated in the simulation section through three numerical examples.

本文研究了二维修正重复控制系统（2D MRCS）的容错和抗干扰衰减问题，该系统由具有多个干扰的切换模糊系统描述。特别地，多重干扰包含外源干扰和标准维纳噪声。具体来说，将广义扩展状态观测器 (GESO) 与 2D MRCS 结合起来，以估计故障和外源多重扰动，以便可以在控制输入中衰减扰动和故障。此外，改进的 2D MRCS 放宽了稳定性条件并提供了增强的跟踪性能。基于 Lyapunov 函数方法、极点放置技术和平均停留时间方法，所考虑系统的稳定性标准是根据线性矩阵不等式 (LMI) 制定的。然后基于获得的 LMI 开发了一种用于设计基于 GESO 的 2D MRC 设计的算法。此外，通过三个数值示例在模拟部分验证了所开发的结果。