This paper investigates the stability issues of model predictive control (MPC) for discrete-time linear systems with state and finite control set (FCS) constraints subject to time-varying disturbances. A new FCS-MPC design and analysis framework is developed using the disturbance estimation approaches and the tool of robust positive invariant (RPI) set sequence. It encompasses a discrete-time exogenous signal observer that helps characterize the estimated dynamics within well-defined bounds and a quantized control law that adheres to both state and input constraints. The practical asymptotical stability of the resulting closed-loop system is shown to be guaranteed, and the tracking error remains uniformly bounded. Finally, simulation results of a numerical example validate the effectiveness of the proposed method.

中文翻译：

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有限控制集约束和干扰下模型预测控制的稳定性


本文研究了具有受时变干扰的状态和有限控制集 （FCS） 约束的离散时间线性系统的模型预测控制 （MPC） 的稳定性问题。使用干扰估计方法和稳健正不变 （RPI） 集合序列工具开发了一种新的 FCS-MPC 设计和分析框架。它包括一个离散时间外生信号观察器，有助于在明确定义的范围内描述估计的动态，以及一个遵守状态和输入约束的量化控制律。结果表明，所得闭环系统的实际渐近稳定性得到了保证，并且跟踪误差保持均匀有界。最后，数值算例的仿真结果验证了所提方法的有效性。