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Input-to-State Stabilization of Linear Systems With Quantized State Measurements

机译：具有量化状态测量的线性系统的输入到状态稳定

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We consider the problem of achieving input-to-state stability (ISS) with respect to external disturbances for control systems with linear dynamics and quantized state measurements. Quantizers considered in this paper take finitely many values and have an adjustable "zoom" parameter. Building on an approach applied previously to systems with no disturbances, we develop a control methodology that counteracts an unknown disturbance by switching repeatedly between "zooming out" and "zooming in." Two specific control strategies that yield ISS are presented. The first one is implemented in continuous time and analyzed with the help of a Lyapunov function, similarly to earlier work. The second strategy incorporates time sampling, and its analysis is novel in that it is completely trajectory-based and utilizes a cascade structure of the closed-loop hybrid system. We discover that in the presence of disturbances, time-sampling implementation requires an additional modification which has not been considered in previous work
机译：对于具有线性动力学和量化状态测量的控制系统，我们考虑了针对外部干扰实现输入状态稳定性（ISS）的问题。本文考虑的量化器采用有限的多个值，并具有可调的“缩放”参数。在先前应用于无干扰系统的方法的基础上，我们开发了一种控制方法，可通过在“缩小”和“放大”之间反复切换来抵消未知干扰。介绍了产生ISS的两种特定控制策略。第一个是连续执行的，并借助Lyapunov函数进行了分析，类似于早期的工作。第二种策略结合了时间采样，其分析是新颖的，因为它完全基于轨迹，并利用了闭环混合系统的级联结构。我们发现，在存在干扰的情况下，时间采样的实现需要进行其他修改，而以前的工作并未对此进行过考虑。

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