Hankel Norm for Nonlinear Digital Systems with Hardware Limitations and External Input

Abstract

This paper concerns the stability behavior of digital systems associated with hardware limitations and implicit nonlinearity. The proposed criterion can be devoted to nonlinear digital systems using overflow arithmetic and external input with an insight to minimize the unwanted memory effects due to previous actions on future outputs. With the established criterion, the reduction of undesired memory effects (system ringing) can be verified through Hankel norm performance of nonlinear digital systems and also the asymptotic stability without external input. In order to validate the optimum reduction of ringing, the work is formulated in linear matrix inequality (LMI)-constraints as convex optimization problem by using Lyapunov theory and Lipschitz condition. Finally, the efficacy and validity of proposed criterion is verified with a numerical example from real nonlinear physical system such as recurrent neural network.