Stability analysis of nonlinear digital systems under hardware overflow constraint for dealing with finite word-length effects of digital technologies

Abstract

The purpose of this paper is to examine stability and originate stability criteria for nonlinear digital systems under the influence of saturation overflow, both in the absence and presence of external interference. The developed approaches can be employed to analyse overflow oscillation-free implementation of a nonlinear digital system under saturation overflow nonlinearity, caused by the finite word-length limitation of a digital hardware, such as computer processor or micro-controller. Asymptotic stability is examined in the absence of disturbance, whereas in the presence of external interference, the form of stability ensured is uniformly ultimately bounded stability, in which the states trajectories converge to an ellipsoidal region around the origin. In most of the studies reported so far, the authors have performed the overflow stability analysis of linear systems but very little (if any) work has been reported on the overflow oscillation elimination (for nonlinear systems). In the present work, sector conditions derived from saturation constraint along with Lipschitz condition are used with a suitable Lyapunov function for the stability analysis of nonlinear digital systems under overflow. The validity and efficacy of these criteria are tested by using examples from real nonlinear physical systems, including Moon chaotic system’s observer and recurrent neural network.