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

Muhammad Umair Amjad, Muhammad Rehan, Muhammad Tufail, Choon Ki Ahn, Haroon Ur Rashid

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)139-148
Number of pages10
JournalSignal Processing
Publication statusPublished - 2017 Nov

Bibliographical note

Funding Information:
This work was supported by the Higher Education Commission of Pakistan and the National Research Foundation of Korea Funded by the Ministry of Science, ICT and Future Planning under Grant NRF-2017R1A1A1A05001325.

Publisher Copyright:
© 2017 Elsevier B.V.


  • Digital hardware overflow
  • Finite word-length effects
  • Linear matrix inequality
  • Nonlinear digital systems
  • Stability analysis

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering


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