A numerical investigation for robust stability of fractional-order uncertain systems

Senol, Bilal; Ateş, Abdullah; Alagöz, Barış Baykant; Yeroğlu, Celaleddin

doi:10.1016/j.isatra.2013.09.004

Cited by 63 publications

(57 citation statements)

References 19 publications

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“…By Theorem 3, the lower and upper limits of this interval are got as R max = 5.8142 × 10 4 and R min = 1.7199 × 10 −5 with η 1 = 80.5, η 2 = 0.0124, ϵ 1 = 0.8 and ϵ 2 = 0.4. Based on the method offered in Senol et al (2014), the number of the vertices with respect to the values set of F (jω) is 16. But 6 redundant vertices are retained, increasing the computational complexity.…”

Section: Robust Stabilization Criterion Of Fractional-order Controllersmentioning

confidence: 99%

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Robust stabilization criterion of fractional-order controllers for interval fractional-order plants

Gao

2015

Automatica

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Section: Robust Stabilization Criterion Of Fractional-order Controllersmentioning

confidence: 99%

“…Meanwhile, a graphical test approach was proposed to test the stability of fractional-order time-delay systems in Yu and Wang (2011). In Senol, Ates, Alagoz, and Yerolu (2014), a numerical approach was given to test the robust stability of fractional-order systems with fractional-order controllers.…”

Section: Introductionmentioning

confidence: 99%

Robust stabilization criterion of fractional-order controllers for interval fractional-order plants

Gao

2015

Automatica

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“…in [65], [66]. The works [49]–[53] extended the concept of the value set to fractional order uncertain polynomials (or quasi-polynomials [58]).…”

Section: Value Sets and Zero Exclusion Conditionmentioning

confidence: 99%

“…Its classical integer order version [33] was extended to the fractional order cases e.g. in [49]–[53]. …”

Section: Introductionmentioning

confidence: 99%

Robust stability of fractional order polynomials with complicated uncertainty structure

Matušů¹,

Senol²,

Pekař³

2017

PLoS ONE

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The main aim of this article is to present a graphical approach to robust stability analysis for families of fractional order (quasi-)polynomials with complicated uncertainty structure. More specifically, the work emphasizes the multilinear, polynomial and general structures of uncertainty and, moreover, the retarded quasi-polynomials with parametric uncertainty are studied. Since the families with these complex uncertainty structures suffer from the lack of analytical tools, their robust stability is investigated by numerical calculation and depiction of the value sets and subsequent application of the zero exclusion condition.

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“…By applying the inverse Laplace transformer to both sides of (4) and using (8), the impulse time domain response is given by …”

Section: Transfer Function In Fractional-order Domainmentioning

confidence: 99%

Fundamentals of fractional‐order LTI circuits and systems: number of poles, stability, time and frequency responses

Semary

Radwan

Hassan

2016

Circuit Theory & Apps

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This paper investigates some basic concepts of fractional-order linear time invariant systems related to their physical and non-physical transfer functions, poles, stability, time domain, frequency domain, and their relationships for different fractional-order differential equations. The analytical formula that calculates the number of poles in physical and non-physical s-plane for different orders is achieved and verified using many practical examples. The stability contour versus the number of poles in the physical s-plane for different fractional-order systems is discussed in addition to the effect of the non-physical poles on the steady state responses. Moreover, time domain responses based on Mittag-Leffler functions for both physical and non-physical transfer functions are discussed for different cases, which confirm the stability analysis. Many fractional-order linear time invariant systems based on fractional-order differential equations have been discussed numerically in both time and frequency domains to validate the previous fundamentals.

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A numerical investigation for robust stability of fractional-order uncertain systems

Cited by 63 publications

References 19 publications

Robust stabilization criterion of fractional-order controllers for interval fractional-order plants

Robust stabilization criterion of fractional-order controllers for interval fractional-order plants

Robust stability of fractional order polynomials with complicated uncertainty structure

Fundamentals of fractional‐order LTI circuits and systems: number of poles, stability, time and frequency responses

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