This paper proposes a novel method to analyze the local stability of Lipschitz nonlinear digital filtering schemes under saturation overflow nonlinearity. Conditions for the stability analysis and robust performance estimation are provided in the form of matrix inequalities by utilizing Lyapunov theory, local saturation overflow arithmetic, and Lipschitz condition. The proposed criterion ascertains (local) asymptotic stability in the absence of perturbations. Under the effects of external interferences, a condition for the local stability, ensuring the H∞ performance objective, is developed. The proposed approach offers a less conservative and more accurate estimate of H∞ performance index than the global method by utilizing a bound on the interferences energy. Moreover, the proposed criterion, in contrast to the existing global methods, can be employed to choose an adequate word length of a digital hardware for the specified values of tolerable perturbations energy, H∞ performance index, and fixed-point resolution. It is worth mentioning that analysis approaches have not been completely reported in the literature, in which local stability criteria for nonlinear discrete-time filtering prototypes under both overflow and disturbances have been developed. A detailed stability analysis for a nonlinear recurrent neural network is performed for demonstrating the effectiveness of the proposed scheme.
Bibliographical noteFunding Information:
The work of C.K. Ahn was supported in part by the National Research Foundation of Korea through the Ministry of Science, ICT and Future Planning under Grant NRF-2017R1A1A1A05001325.
© 2018 Elsevier B.V.
Copyright 2018 Elsevier B.V., All rights reserved.
- External interferences
- H performance
- Lipschitz digital filters
- Local stability
- Saturation overflow
ASJC Scopus subject areas
- Control and Systems Engineering
- Signal Processing
- Computer Vision and Pattern Recognition
- Electrical and Electronic Engineering