Local stability analysis and H_∞ performance for Lipschitz digital filters with saturation nonlinearity and external interferences

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.