this paper presents the basic concepts of stability in fuzzy linguistic models. theauthors have proposed a criterion for bibo stability analysis of fuzzy linguistic modelsassociated to linear time invariant systems [25]-[28]. this paper presents the basic concepts ofstability in the general nonlinear and linear systems. this stability analysis method is verifiedusing a benchmark system analysis.

The classic equation for decomposing the wavefront aberrations of axis-symmetrical optical systems has form, $$ W({h}_0,\rho,\phi )=\sum_{j=0}^{\propto } \sum_{p=0}^{\propto \sum_{m=0}^{\propto {C}_{\left(2j+m\right)\left(2p+m\right)m}({h}_0{)}^{2j+m}(\rho {)}^{2p+m}(\mathrm{cos}\phi {)}^m where j , p and m are non-negative integers, ρ ϕ polar coordinates pupil, h 0 is object height. However, o...

Abstract We consider a homogeneous differential operator $${\mathcal {A}}$$ A and show an improved version of Murat’s condition for -quasiaffine functions, provided that the satisfies constant rank condition. As consequence, we obtain affinity along characteristic cone implies -quasiaffinity if admits first o...