Fractional difference inequalities with their implications to the stability analysis of nabla fractional order systems

2021 ◽  
Author(s):  
Yiheng Wei
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Fractional Order Systems ◽  
Fractional Difference ◽  
The Stability

Stability analysis of conformable fractional-order nonlinear systems depending on a parameter

2020 ◽  
Vol 26 (2) ◽  
pp. 287-296
Author(s):  
O. Naifar ◽  
G. Rebiai ◽  
A. Ben Makhlouf ◽  
M. A. Hammami ◽  
A. Guezane-Lakoud
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Fractional Order ◽  
Feedback Controller ◽  
Fractional Order Systems ◽  
The Stability

AbstractIn this paper, the stability of conformable fractional-order nonlinear systems depending on a parameter is presented and described. Furthermore, The design of a feedback controller for the same class of conformable fractional-order systems is introduced. Illustrative examples are given at the end of the paper to show the effectiveness of the proposed results.

Robust Stability Analysis of Uncertain Linear Fractional-Order Systems With Time-Varying Uncertainty for 0 < α < 2

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Mohammad Tavazoei ◽  
Mohammad Hassan Asemani
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Robust Stability ◽  
Stability Condition ◽  
Upper Bound ◽  
Order System ◽  
Time Varying ◽  
Fractional Order Systems ◽  
Robust Stability Analysis ◽  
The Stability

This paper focuses on the stability analysis of linear fractional-order systems with fractional-order 0<α<2, in the presence of time-varying uncertainty. To obtain a robust stability condition, we first derive a new upper bound for the norm of Mittag-Leffler function associated with the nominal fractional-order system matrix. Then, by finding an upper bound for the norm of the uncertain fractional-order system solution, a sufficient non-Lyapunov robust stability condition is proposed. Unlike the previous methods for robust stability analysis of uncertain fractional-order systems, the proposed stability condition is applicable to systems with time-varying uncertainty. Moreover, the proposed condition depends on the fractional-order of the system and the upper bound of the uncertainty matrix norm. Finally, the offered stability criteria are examined on numerical uncertain linear fractional-order systems with 0<α<1 and 1<α<2 to verify the applicability of the proposed condition. Furthermore, the stability of an uncertain fractional-order Sallen–Key filter is checked via the offered condition.

Non-smooth convex Lyapunov functions for stability analysis of fractional-order systems

2018 ◽  
Vol 41 (6) ◽  
pp. 1627-1639 ◽  
Author(s):  
Aldo-Jonathan Muñoz-Vázquez ◽  
Vicente Parra-Vega ◽  
Anand Sánchez-Orta
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Lyapunov Functions ◽  
Sliding Mode ◽  
Unit Vector ◽  
Sliding Mode Controller ◽  
Fractional Order Systems ◽  
Analysis And Design ◽  
Bounded Disturbances ◽  
The Stability

Based on proximal subdifferentials and subgradients, and instrumented with an extended Caputo differintegral operator, the stability analysis of a general class of fractional-order nonlinear systems is considered by means of non-smooth but convex Lyapunov functions. This facilitates concluding the Mittag–Leffler stability for fractional-order systems whose solutions are not necessarily differentiable in any integer-order sense. As a solution to the problem of robust command of fractional-order systems subject to unknown but Lebesgue-measurable and bounded disturbances, a unit-vector-like integral sliding mode controller is proposed. Numerical simulations are conducted to highlight the reliability of the proposed method in the analysis and design of fractional-order systems closed by non-smooth robust controllers.

Large-scale fractional-order systems: stability analysis and their decentralised functional observers design

2018 ◽  
Vol 12 (3) ◽  
pp. 359-367 ◽  
Author(s):  
Yassine Boukal ◽  
Mohamed Darouach ◽  
Michel Zasadzinski ◽  
Nour-Eddine Radhy
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Large Scale ◽  
Fractional Order Systems

Stability of Nonlinear Fractional-Order Time Varying Systems

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Sunhua Huang ◽  
Runfan Zhang ◽  
Diyi Chen
Keyword(s):  
Laplace Transform ◽  
Fractional Order ◽  
Caputo Derivative ◽  
Local Stability ◽  
State Feedback ◽  
Sufficient Condition ◽  
Time Varying ◽  
Fractional Order Systems ◽  
Time Varying Systems ◽  
The Stability

This paper is concerned with the stability of nonlinear fractional-order time varying systems with Caputo derivative. By using Laplace transform, Mittag-Leffler function, and the Gronwall inequality, the sufficient condition that ensures local stability of fractional-order systems with fractional order α : 0<α≤1 and 1<α<2 is proposed, respectively. Moreover, the condition of the stability of fractional-order systems with a state-feedback controller is been put forward. Finally, a numerical example is presented to show the validity and feasibility of the proposed method.

A Survey of Fractional-Order Neural Networks

2017 ◽  
Author(s):  
Shuo Zhang ◽  
YangQuan Chen ◽  
Yongguang Yu
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Fractional Order ◽  
Computational Science ◽  
General Introduction ◽  
Analysis Methods ◽  
Recent Trends ◽  
The Stability

In this paper, the literature of fractional-order neural networks is categorized and discussed, which includes a general introduction and overview of fractional-order neural networks. Various application areas of fractional-order neural networks have been found or used, and will be surveyed and summarized such as neuroscience, computational science, control and optimization. Recent trends in dynamics of fractional-order neural networks are presented and discussed. The results, especially the stability analysis of fractional-order neural networks, are reviewed and different analysis methods are compared. Furthermore, the challenges and conclusions of fractional-order neural networks are given.

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