Improved Hankel Norm Criterion for Interfered Nonlinear Digital Filters Subjected to Hardware Constraints

Abstract

This article considers the global stability analysis of interfered nonlinear digital filtering schemes implemented with fixed-point arithmetic. The proposed approach uses Hankel norm to verify the reduction of undesired memory effects of previous inputs (ringing) on future responses in nonlinear digital filters with saturation overflow nonlinearity and external disturbance. Also, the proposed criterion verifies the asymptotic stability of nonlinear digital filter without external disturbance. With the obtained results, it is shown that the suggested criterion is less restrictive than the existing criterion in the literature. By using Lyapunov stability theory, sector-based saturation nonlinearity, and Lipschitz continuity, the approach is framed in linear matrix inequality (LMI)-constraints. The efficacy, validity, and reduced conservatism of presented criterion are tested with two numerical examples.