This paper deals with the robust stabilization of uncertain discrete-time switched affine systems using a control Lyapunov approach and a min-switching state-feedback control law. After presenting some preliminaries on limit cycles, a constructive stabilization theorem, expressed as linear matrix inequalities, guarantees that the solutions to the nominal closed-loop system converge to a limit cycle. This method is extended to the case of uncertain systems, for which the notion of limit cycle needs to be adapted. The theoretical results are evaluated on academic examples and demonstrate the potential of the method over the recent literature.

中文翻译：

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离散时间切换仿射系统的吸引子和极限环：标称和不确定情况

本文使用控制 Lyapunov 方法和最小切换状态反馈控制律处理不确定离散时间切换仿射系统的稳健稳定性。在介绍了一些关于极限环的预备知识之后，构造性稳定定理（表示为线性矩阵不等式）保证标称闭环系统的解收敛到极限环。该方法扩展到不确定系统的情况，为此需要调整极限环的概念。理论结果在学术实例上进行了评估，并证明了该方法在最近文献中的潜力。