This work addresses stability of interfered digital filters with state-delay and saturation arithmetic. By utilizing a quadratic Lyapunov functional and properties of saturation overflow, a new condition is established to ensure stability of interfered digital filters under the influence of saturation arithmetic and state-delay. The criterion is capable of finding minimum \(H_\infty \) norm in the existence of external disturbance and ensures exponential stability in the nonexistence of disturbance. Further, an improved condition is obtained to ensure asymptotic stability of digital filters with saturation arithmetic. The established conditions are in linear matrix inequality framework and therefore computationally less demanding. It is shown that the stability criteria presented in this study are less stringent than few existing stability results. With the help of numerical examples, superiority of the presented approach is demonstrated.

这项工作通过状态延迟和饱和算法解决了受干扰数字滤波器的稳定性。通过利用二次Lyapunov函数和饱和溢出特性，建立了一个新条件，以确保在饱和算术和状态延迟的影响下受干扰的数字滤波器的稳定性。该标准能够找到最小\（H_ \ infty \）规范外部干扰的存在，并确保不存在干扰时的指数稳定性。此外，获得了改善的条件，以确保具有饱和算法的数字滤波器的渐近稳定性。所建立的条件在线性矩阵不等式框架中，因此对计算的要求较低。结果表明，这项研究提出的稳定性标准比现有的稳定性结果要严格一些。借助数值示例，证明了所提出方法的优越性。