This paper presents passivity-based results to address stability of interfered digital filters with state-delay and saturation nonlinearities. A very-strict passivity condition is proposed for the digital filters by using an appropriate Lyapunov-Krasovskii functional. The established criterion ensures limit-cycle free realization of state-delayed interfered digital filters using saturation arithmetic. Conditions for passivity, input-strict passivity and output-strict passivity of the digital filters are obtained as special cases of the proposed result. In addition, an asymptotic stability condition for the digital filters with zero external interference is presented. It is also demonstrated that a stability condition reported in a recent work may be recovered from the established criterion. Numerical simulations are given to demonstrate worthiness of the proposed results.

中文翻译：

---

受外部干扰和状态延迟影响的数字滤波器的稳定性

本文提出了基于无源性的结果，以解决具有状态延迟和饱和非线性的受干扰数字滤波器的稳定性问题。通过使用适当的 Lyapunov-Krasovskii 泛函，为数字滤波器提出了非常严格的无源条件。建立的标准确保使用饱和算法实现状态延迟干扰数字滤波器的无极限循环。数字滤波器的无源性、输入严格无源性和输出严格无源性条件作为建议结果的特例获得。此外，还提出了具有零外部干扰的数字滤波器的渐近稳定性条件。还证明了在最近的工作中报告的稳定性条件可以从既定的标准中恢复。