Stability and stabilization for linear state feedback control systems in the presence of sensor quantization are studied. As the closed-loop system is described by a discontinuous right-hand side differential equation, Krasovskii solutions (to the closed-loop system) are considered. Sufficient conditions in the form of matrix inequalities are proposed to characterize uniform global asymptotic stability of a compact set containing the origin. Such conditions are shown to be always feasible whenever the quantization-free closed-loop system is asymptotically stable. Building on the obtained conditions, computationally affordable algorithms for the solution to the considered problems are illustrated. The effectiveness of the proposed methodology is shown in three examples.

中文翻译：

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关于线性控制系统中的传感器量化：Krasovskii解决方案满足半定编程

研究了存在传感器量化的线性状态反馈控制系统的稳定性和稳定性。由于闭环系统由不连续的右侧微分方程描述，因此考虑了Krasovskii解（针对闭环系统）。提出了矩阵不等式形式的充分条件，以表征包含原点的紧集的一致全局渐近稳定性。当无量化闭环系统渐近稳定时，这种条件总是可行的。在获得的条件的基础上，说明了用于解决所考虑问题的计算上可承受的算法。所提出的方法的有效性在三个示例中显示。