scholarly journals Value-Set-Based Approach to Robust Stability Analysis for Ellipsoidal Families of Fractional-Order Polynomials with Complicated Uncertainty Structure

2019 ◽  
Vol 9 (24) ◽  
pp. 5451 ◽  
Author(s):  
Radek Matušů ◽  
Bilal Şenol ◽  
Libor Pekař
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Robust Stability ◽  
Linear Time ◽  
Complex Structure ◽  
Parametric Uncertainty ◽  
Value Set ◽  
Uncertainty Structure ◽  
Robust Stability Analysis ◽  
Exclusion Condition

This paper presents the application of a value-set-based graphical approach to robust stability analysis for the ellipsoidal families of fractional-order polynomials with a complex structure of parametric uncertainty. More specifically, the article focuses on the families of fractional-order linear time-invariant polynomials with affine linear, multilinear, polynomic, and general uncertainty structure, combined with the uncertainty bounding set in the shape of an ellipsoid. The robust stability of these families is investigated using the zero exclusion condition, supported by the numerical computation and visualization of the value sets. Four illustrative examples are elaborated, including the comparison with the families of fractional-order polynomials having the standard box-shaped uncertainty bounding set, in order to demonstrate the applicability of this method.

scholarly journals Robust Stability of Fractional-Order Linear Time-Invariant Systems: Parametric versus Unstructured Uncertainty Models

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Radek Matušů ◽  
Bilal Şenol ◽  
Libor Pekař
Keyword(s):  
Fractional Order ◽  
Robust Stability ◽  
Linear Time ◽  
Parametric Uncertainty ◽  
Uncertainty Modeling ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Robust Stability Analysis ◽  
Uncertainty Models ◽  
Time Invariant

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.

Robust stability analysis of uncertain incommensurate fractional order quasi- polynomials in the presence of interval fractional orders and interval coefficients

2020 ◽  
pp. 014233122096896
Author(s):  
Majid Ghorbani ◽  
Mahsan Tavakoli-Kakhki
Keyword(s):  
Stability Analysis ◽  
Computational Complexity ◽  
Fractional Order ◽  
Robust Stability ◽  
General Type ◽  
Value Set ◽  
Interval Uncertainties ◽  
Robust Stability Analysis ◽  
Interval Coefficients ◽  
Fractional Orders

This paper deals with the robust stability analysis of a class of incommensurate fractional order quasi-polynomials with a general type of interval uncertainties. The concept of the general type of interval uncertainties means that all the coefficients and orders of the fractional order quasi-polynomials have interval uncertainties. Generally, the computational complexity of specifying the robust stability of such a quasi-polynomial is shown in this paper. To this end, the robust stability is studied by Principle of Argument theorem. In fact, by presenting two theorems and three lemmas it is shown that the robust stability of a fractional order quasi-polynomial involving the general type of uncertainty can be simply investigated without needing to plot its value set by heavy computations. Examples are attested the validity of the paper results.

Robust Stability Analysis of Interval Fractional-Order Plants with Interval Time delay and General Form of Fractional-Order Controllers

2021 ◽  
pp. 1-1
Author(s):  
Majid Ghorbani ◽  
Mahsan Tavakoli-Kakhki ◽  
Aleksei Tepljakov ◽  
Eduard Petlenkov ◽  
Arash Farnam ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Fractional Order ◽  
Robust Stability ◽  
Interval Time ◽  
Robust Stability Analysis

Robust stability analysis of fractional order interval polynomials

2009 ◽  
Vol 48 (2) ◽  
pp. 166-172 ◽  
Author(s):  
Nusret Tan ◽  
Ö. Faruk Özgüven ◽  
M. Mine Özyetkin
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Robust Stability ◽  
Order Interval ◽  
Robust Stability Analysis ◽  
Interval Polynomials

Large-Scale Power System Robust Stability Analysis Based on Value Set Approach

2017 ◽  
Vol 32 (5) ◽  
pp. 4012-4023 ◽  
Author(s):  
Jinghao Zhou ◽  
Peng Shi ◽  
Deqiang Gan ◽  
Ying Xu ◽  
Huanhai Xin ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Power System ◽  
Robust Stability ◽  
Large Scale ◽  
Value Set ◽  
Robust Stability Analysis
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