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

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.