Delay-Dependent Stability Analysis of Interfered Digital Filters with Time-Varying Delay and Saturation Nonlinearities

This work investigates stability of interfered digital filters with time-varying delay and saturation overflow arithmetic. A criterion is proposed to guarantee exponential stability of the state-delayed digital filters with saturation nonlinearities and external disturbance. The established condition is utilized to obtain the H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\infty $$\end{document} performance norm of the interfered digital filters employing saturation arithmetic. Further, a result is developed for the asymptotic stability of interference-free digital filters with zero state-delay. The criterion presented for the digital filters employing saturation arithmetic is shown to be less conservative than the existing works. All the stability conditions are in the form of linear matrix inequalities framework and thus readily solvable. Numerical examples are given to illustrate the merit and efficiency of the established criteria.