An output sensitivity problem for a class of fractional order discrete-time linear systems

• Autorzy: Benfatah Youssef , El-Bhih Amine , Rachik Mostafa , Lafif Marouane

Identyfikatory

DOI

10.2478/ama-2021-0029

• Języki publikacji: EN

Abstrakty

EN

Consider the linear discrete-time fractional order systems with uncertainty on the initial state {Δαxi+1=Axi+Bui, i≥0x0=τ0+τ̂0∈Rn, τ̂0∈Ωyi=Cxi, i≥0}, where A,B and C are appropriate matrices, x0 is the initial state, yi is the signal output, α the order of the derivative, τ0 and τ̂0 are the known and unknown part of x0, respectively, ui=Kxi is feedback control and Ω⊂Rn is a polytope convex of vertices w1,w2,...,wp. According to the Krein–Milman theorem, we suppose that τ̂0=Σ pj=1αjwj for some unknown coefficients α1≥0,...,αp≥0 such that Σ pj=1αj=1. In this paper, the fractional derivative is defined in the Grünwald–Letnikov sense. We investigate the charac-terisation of the set χ(τ̂0,ϵ) of all possible gain matrix K that makes the system insensitive to the unknown part τ̂0, which means χ(τ̂0,ϵ)={K∈Rm×n / ∥∂yi∂αj∥≤ϵ, ∀j=1,...,p,∀i≥0}, where the inequality ∥∂yi∂αj∥≤ϵ showing the sensitivity of yi relative-ly to uncertainties {αj}j=1p will not achieve the specified threshold ϵ>0. We establish, under certain hypothesis, the finite determination of χ(τ̂0,ϵ) and we propose an algorithmic approach to made explicit characterisation of such set.

Słowa kluczowe

EN

fractional order systems; output sensitivity; discrete time systems; maximal output set admissible uncertainty

• Wydawca: Oficyna Wydawnicza Politechniki Białostockiej
• Czasopismo: Acta Mechanica et Automatica
• Rocznik: 2021
• Tom: Vol. 15, no. 4
• Strony: 227--235
• Opis fizyczny: Bibliogr. 38 poz., rys., wykr.

Twórcy

autor

Benfatah Youssef

• Faculty of Sciences Ben M’Sik, Department of Mathematics and Computer Science, Hassan II University, Casablanca, Sidi Othman BP 7955, Morocco

• https://orcid.org/0000-0001-9497-003X

autor

El-Bhih Amine

• Faculty of Sciences Ben M’Sik, Department of Mathematics and Computer Science, Hassan II University, Casablanca, Sidi Othman BP 7955, Morocco

• https://orcid.org/0000-0003-0877-5882

autor

Rachik Mostafa

• Faculty of Sciences Ben M’Sik, Department of Mathematics and Computer Science, Hassan II University, Casablanca, Sidi Othman BP 7955, Morocco

• https://orcid.org/0000-0002-5118-2786

autor

Lafif Marouane

• Faculty of Sciences Ben M’Sik, Department of Mathematics and Computer Science, Hassan II University, Casablanca, Sidi Othman BP 7955, Morocco

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