In this paper, the robust digital stabilization problem of nonlinear systems is investigated. In particular, a methodology for the design of robust quantized sampled-data stabilizers updated via an event-triggered mechanism is provided for time-varying control-affine nonlinear systems affected by actuation disturbances and measurement noises. The notion of time-varying steepest descent feedback (TSDF), continuous or not, and the Input-to-State Stability (ISS) redesign methodology are used for the development of the proposed robust event-based digital controller. Under the assumption that the actuation disturbances and measurement noises are bounded with a-priori known bounds and that the amplitude of the measurement noises satisfies a certain condition related to the new added robustification term, the following result is proved: there exist a suitably fast sampling and an accurate quantization of the input/output channels such that the digital implementation of robustified TSDF controllers, updated through a proposed event-triggered mechanism, ensures semi-global practical stability of the related closed-loop system regardless of the above uncertainties. In the methodology here proposed, time-varying sampling periods and the non-uniform quantization of the input/output channels are allowed. Moreover, the theory here developed includes the analysis of the intersampling system behaviour. Possible discontinuities in the function describing the TSDF at hand are also managed. The provided results are validated through a numerical example.

中文翻译：

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控制仿射非线性系统的基于数字事件的控制器的鲁棒性


本文研究了非线性系统的鲁棒数字镇定问题。特别是，为受驱动干扰和测量噪声影响的时变控制仿射非线性系统提供了一种通过事件触发机制更新的鲁棒量化采样数据稳定器的设计方法。时变最速下降反馈（TSDF）（连续或非连续）的概念以及输入状态稳定性（ISS）重新设计方法用于开发所提出的基于事件的鲁棒数字控制器。假设驱动干扰和测量噪声均以先验已知界限为界，并且测量噪声的幅度满足与新添加的鲁棒性项相关的一定条件，则证明以下结果：存在适当的快速采样输入/输出通道的精确量化，使得鲁棒的 TSDF 控制器的数字实现，通过所提出的事件触发机制进行更新，确保相关闭环系统的半全局实际稳定性，而不管上述不确定性如何。在这里提出的方法中，允许时变采样周期和输入/输出通道的非均匀量化。此外，这里开发的理论包括对内部采样系统行为的分析。描述现有 TSDF 的函数中可能存在的不连续性也得到了管理。通过数值示例验证了所提供的结果。