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.

scholarly journals Robust Stability Analysis of Nonlinear Fractional-Order Time-Variant Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Chen Caixue ◽  
Xie Yunxiang
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Robust Stability ◽  
State Feedback ◽  
Stability Theorem ◽  
Feedback Controller ◽  
Sufficient Condition ◽  
Fractional Order Systems ◽  
Numerical Example ◽  
Robust Stability Analysis

This paper presents a stability theorem for a class of nonlinear fractional-order time-variant systems with fractional orderα  (1<α<1)by using the Gronwall-Bellman lemma. Based on this theorem, a sufficient condition for designing a state feedback controller to stabilize such fractional-order systems is also obtained. Finally, a numerical example demonstrates the validity of this approach.

scholarly journals Stability Analysis of Fractional-Order Nonlinear Systems with Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yu Wang ◽  
Tianzeng Li
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Fractional Order ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Delay System ◽  
Fractional Order Systems ◽  
Lyapunov Direct Method ◽  
Definition Of ◽  
Fractional Order Nonlinear System

Stability analysis of fractional-order nonlinear systems with delay is studied. We propose the definition of Mittag-Leffler stability of time-delay system and introduce the fractional Lyapunov direct method by using properties of Mittag-Leffler function and Laplace transform. Then some new sufficient conditions ensuring asymptotical stability of fractional-order nonlinear system with delay are proposed firstly. And the application of Riemann-Liouville fractional-order systems is extended by the fractional comparison principle and the Caputo fractional-order systems. Numerical simulations of an example demonstrate the universality and the effectiveness of the proposed method.

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.

scholarly journals Observer-based adaptive neural network backstepping sliding mode control for switched fractional order uncertain nonlinear systems with unmeasured states

2021 ◽  
pp. 002029402110211
Author(s):  
Tao Chen ◽  
Damin Cao ◽  
Jiaxin Yuan ◽  
Hui Yang
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Tracking Error ◽  
Adaptive Neural Network ◽  
Dynamic Surface ◽  
Mode Control ◽  
The Stability

This paper proposes an observer-based adaptive neural network backstepping sliding mode controller to ensure the stability of switched fractional order strict-feedback nonlinear systems in the presence of arbitrary switchings and unmeasured states. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. An observer is used for states estimation of the fractional order systems. The sliding mode control technology is introduced to enhance robustness. The unknown nonlinear functions and uncertain disturbances are approximated by the radial basis function neural networks (RBFNNs). The stability of system is ensured by the constructed Lyapunov functions. The fractional adaptive laws are proposed to update uncertain parameters. The proposed controller can ensure convergence of the tracking error and all the states remain bounded in the closed-loop systems. Lastly, the feasibility of the proposed control method is proved by giving two examples.

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
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