An Optimal H∞ Approach for Local Stability Analysis of Non Linear Digital Systems with Saturation Non Linearity and External Interference

Abstract

An optimal [Formula: see text] criterion for the stability investigation of non linear digital filters with saturation non linearity and external interference is proposed in this paper. The proposed criterion can be used for overflow oscillation-free realization of the non linear digital system implemented with fixed wordlength machines like digital computers or special purpose embedded systems. The proposed approach ascertains the local asymptotic stability of non linear digital filtering schemes without external interference. Further, by employing [Formula: see text] performance criterion the conditions for local stability and performance measurement are proposed with external interference. In the proposed work, the stability conditions are proposed in linear matrix inequality (LMI) by exploiting energy-based Lyapunov theory, Lipschitz inequality, and saturation arithmetic. The proposed criterion is shown to be less conservative which will improve the operating region and obtain a better estimate of [Formula: see text] performance index compared to the existing local criterion. Moreover, the proposed criterion can be used in selecting the appropriate wordlength of a digital system for tolerable values of interference energy, [Formula: see text] performance level, and fixed-point resolution. This will be an additional advantage of this work compared with existing global criteria. Sufficient examples to show the efficacy of the proposed technique are also provided.