Robust stability criterion for fractional-order systems with interval uncertain coefficients and a time-delay

Gao, Zhe

doi:10.1016/j.isatra.2015.05.019

Cited by 25 publications

(24 citation statements)

References 31 publications

(36 reference statements)

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“…The field of control theory is no exception to this trend. Control researchers exploit benefits of differentiation and integration under an arbitrary real or even complex number, and thus, many related scientific control-oriented works have appeared recently [15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Robust Stability of Fractional‐Order Linear Time‐Invariant Systems: Parametric versus Unstructured Uncertainty Models

2018

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The main aim of this paper is to present and compare three approaches to uncertainty modeling and robust stability analysis for fractional-order (FO) linear time-invariant (LTI) single-input single-output (SISO) uncertain systems. The investigated objects are described either via FO models with parametric uncertainty, by means of FO unstructured multiplicative uncertainty models, or through FO unstructured additive uncertainty models, while the unstructured models are constructed on the basis of appropriate selection of a nominal plant and a weight function. Robust stability investigation for systems with parametric uncertainty uses the combination of plotting the value sets and application of the zero exclusion condition. For the case of systems with unstructured uncertainty, the graphical interpretation of the utilized robust stability test is based mainly on the envelopes of the Nyquist diagrams. The theoretical foundations are followed by two extensive, illustrative examples where the plant models are created; the robust stability of feedback control loops is analyzed, and obtained results are discussed.

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Section: Introductionmentioning

confidence: 99%

Robust Stability of Fractional‐Order Linear Time‐Invariant Systems: Parametric versus Unstructured Uncertainty Models

2018

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“…For a fractional‐order control system, maintaining the stability of the closed‐loop system is an essential task. () Moreover, the control system often suffers from uncertainties due to modeling errors, variations of operating conditions, and manufacturing tolerances. Therefore, recently the subject of robust stability and stabilization problem for the uncertain fractional‐order system has received an increasing attention.…”

Section: Introductionmentioning

confidence: 99%

“…It plots the value set of the characteristic function of the interval fractional system at each frequency and then checks whether zero is excluded by the value set. The advantage of the graphical method is that it can present necessary and sufficient conditions to the stabilization of some certain types of interval fractional system such as fractional system with incommensurate order and fractional delay system. Gao() presented efficient criteria to test the stability/stabilization of interval fractional system with/without time delay.…”

Section: Introductionmentioning

confidence: 99%

“…The advantage of the graphical method is that it can present necessary and sufficient conditions to the stabilization of some certain types of interval fractional system such as fractional system with incommensurate order and fractional delay system. Gao() presented efficient criteria to test the stability/stabilization of interval fractional system with/without time delay. In the work of Zheng et al,() graphical tuning methods were proposed to compute the exact stabilizing region of PID controllers for the interval fractional system.…”

Section: Introductionmentioning

confidence: 99%

“…However, this work conducts a detail study on the computational issue of the stabilization test. As indicated in the work of Gao, the computational issue is a very important aspect for the graphical method, and improving the computational efficiency of the graphical approach is a nontrivial task.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust stabilization of fractional‐order plant with general interval uncertainties based on a graphical method

Zheng

2017

Intl J Robust & Nonlinear

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This paper concentrates on the robust stabilization of fractional-order plant suffering from general interval uncertainties by using fractional-order controllers.General interval uncertainties mean that the coefficients and orders of the denominator and nominator of the fractional-order plant are all uncertain and lie in specified intervals. Two main contributions are presented, as follows.(i) Based on a graphical method, a necessary and sufficient criterion is proposed for the stabilization of the general interval fractional-order plant. By adopting some well-defined multivalue functions, the proposed method can explicitly construct the nonconvex boundary of the value set of the fractional system.(ii) Two alternative methods are presented to improve the computational efficiency of the stabilization test. Based on a newly developed redundancy elimination technique, the first method can avoid computing and plotting many segments, which are in the interior of the value set of the fractional system. The second method utilizes a novel convex polygon bounding approach. It can efficiently construct a convex polygon to bound the nonconvex value set of the general interval fractional system. Examples are followed to illustrate the effectiveness of the proposed methods.

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Robust stability analysis of a general class of interval delayed fractional order plants by a general form of fractional order controllers

Ghorbani

Tavakoli-Kakhki

2021

Math Methods in App Sciences

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In this paper, the robust stability of interval fractional order plants with one time delay controlled by fractional order controllers is investigated in a general form. For robust stability analysis of the closed loop system by the zero exclusion principle, the distance between the origin and the value set of the characteristic function needs to be checked. It is known that the outer vertices of this value set may change at some switching frequencies and the repetitive calculation of these vertices at switching frequencies leads to additional calculations. In this study initially, new necessary and sufficient conditions are proposed to check the robust stability of a delayed fractional order closed loop system. Then, a novel robust stability testing function is presented based on some vertices, which are fixed for all positive frequencies. Therefore, no additional calculation is needed to obtain the outer vertices of the characteristic function value set for any pair of the switching frequencies. Also, a finite frequency range is presented to reduce the computational cost noticeably. Eventually, three numerical examples are given to verify the efficiency of the results of this paper.

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Robust stability criterion for fractional-order systems with interval uncertain coefficients and a time-delay

Cited by 25 publications

References 31 publications

Robust Stability of Fractional‐Order Linear Time‐Invariant Systems: Parametric versus Unstructured Uncertainty Models

Robust Stability of Fractional‐Order Linear Time‐Invariant Systems: Parametric versus Unstructured Uncertainty Models

Robust stabilization of fractional‐order plant with general interval uncertainties based on a graphical method

Robust stability analysis of a general class of interval delayed fractional order plants by a general form of fractional order controllers

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