ISS Criterion for Lipschitz Nonlinear Interfered Fixed-Point Digital Filters with Saturation Overflow Arithmetic

In this paper, we study the problem of input-to-state stability (ISS) of Lipschitz nonlinear fixed-point digital filters in a state-space realization with saturation arithmetic and external disturbance. Using the Lyapunov theory along with the 'passivity property' of saturation nonlinearities and the Lipschitz condition, a new criterion for the ISS of such digital filters is established. The criterion can be used to confirm the diminishing effect of external interference as well as to guarantee the asymptotic stability of digital filters in the absence of interference. Suitable examples are given to illustrate the efficacy of the proposed approach.

Automated summary

This paper investigates the input-to-state stability (ISS) of Lipschitz nonlinear fixed-point digital filters in a state-space realization with saturation arithmetic and external disturbance, establishing a new criterion for ISS using Lyapunov theory and the 'passivity property' of saturation nonlinearities and Lipschitz condition. The criterion confirms the diminishing effect of external interference and guarantees the asymptotic stability of digital filters in the absence of interference, with suitable examples provided to illustrate the effectiveness of the proposed approach.