Criterion for the Global Asymptotic Stability of Fixed-Point Lipschitz Nonlinear Digital Filter with 2’s Complement Overflow Arithmetic

Abstract

This paper is concerned with the global asymptotic stability (GAS) problem of fixed-point Lipschitz nonlinear digital filters employing 2’s complement overflow arithmetic. Nonlinear digital filtering finds immense applications in various fields such as adaptive systems and controllers, digital controllers and observers for nonlinear systems, realization of neural networks using digital hardware, controllers for feedback linearization, etc. Lipschitz nonlinear digital filter is considered in this paper as it is frequently employed in nonlinear digital filtering, state filtering, neural networks, feedback control, digital controllers, decision-taking systems and so on. Based on Lyapunov theory, the property of 2’s complement overflow arithmetic and Lipschitz condition associated with system nonlinearities, a new criterion for the suppression of overflow oscillations in 2’s complement state variable realizations of digital filters is established. Several examples along with simulation results are provided to highlight the utility of the criterion.