In this paper, the stability of linear systems with sawtooth input delay widely existing in networked systems and predictor-based controller is considered. Under the assumption that there exists an instant where the input delay is zero, a necessary and sufficient condition is obtained to guarantee the exponential stability of the closed-loop system, that is, the closed-loop system is stable if and only if the matrix $A+BK$ is Hurwitz. Two simulation examples are given to confirm the validity of the obtained results.

中文翻译：

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具有锯齿输入延迟和基于预测器的控制器的线性系统的稳定性

在本文中，考虑了在网络系统和基于预测器的控制器中广泛存在的具有锯齿输入延迟的线性系统的稳定性。在存在输入延迟为零的瞬间的假设下，获得必要的充分条件以保证闭环系统的指数稳定性，即，当且仅当矩阵为负时，闭环系统才稳定$\mathrm{一种}+乙ķ$是赫维兹。给出两个仿真实例，以验证所获得结果的有效性。