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Soft Computing

, Volume 23, Issue 21, pp 11247–11262 | Cite as

Revised convexity, normality and stability properties of the dynamical feedback fuzzy state space model (FFSSM) of insulin–glucose regulatory system in humans

  • Izaz Ullah KhanEmail author
  • Tahir Ahmad
  • Normah Maan
Methodologies and Application
  • 67 Downloads

Abstract

This research tries to explore more important structural properties of the insulin–glucose regulatory system in humans. Consequently, an important theorem, namely “revised modified optimized defuzzified value theorem” for feedback systems is derived and then proved. Moreover, the properties concerning the convexity, normality and the bounded-input bounded-output stability of the induced solution of FFSSM are researched. The proposed theorems and lemmas are successfully implemented and verified for the insulin–glucose system in humans. The successful and promising results and proofs of the theorems of the relevant properties improve the credibility and reliability of the FFSSM model of the insulin–glucose regulatory system in humans.

Keywords

Insulin–glucose regulations Feedback systems Fuzzy state space model (FSSM) Inverse modeling Dynamical systems Modern control theory 

Notes

Acknowledgements

We are thankful to the respectable editors and reviewers for their relevant, credible and useful reviews and suggestions. Thanks are due to COMSATS University Islamabad, Abbottabad Campus, Pakistan, and UTM Malaysia.

Funding

This study was funded by no agency/grant.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors. The data presented are obtained from the widely accepted published research Sturis (1991), Sturis et al. (1991) and Tolić et al. (2000).

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsCOMSATS University IslamabadAbbottabadPakistan
  2. 2.Department of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi MalaysiaSkudaiMalaysia

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