scholarly journals New Stability Tests for Discretized Fractional-Order Systems Using the Al-Alaoui and Tustin Operators

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Rafał Stanisławski ◽  
Marek Rydel ◽  
Krzysztof J. Latawiec
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Fractional Order Systems ◽  
Simulation Experiments ◽  
Stability Tests ◽  
Analytical Stability ◽  
Discrete Time Systems ◽  
The Stability ◽  
Time Systems ◽  
Order Continuous

This paper provides new results on a stable discretization of commensurate fractional-order continuous-time LTI systems using the Al-Alaoui and Tustin discretization methods. New, graphical, and analytical stability/instability conditions are given for discrete-time systems obtained by means of the Al-Alaoui discretization scheme. On this basis, an analytically driven stability condition for discrete-time systems using the Tustin-based approach is presented. Finally, the stability of discrete-time systems obtained by finite-length approximation of the Al-Alaoui and Tustin operators are discussed. Simulation experiments confirm the effectiveness of the introduced stability tests.

scholarly journals Generalized convergence analysis of the fractional order systems

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 404-411
Author(s):  
Ahmad Ruzitalab ◽  
Mohammad Hadi Farahi ◽  
Gholamhossien Erjaee
Keyword(s):  
Fractional Order ◽  
Fractional Order Systems ◽  
Necessary And Sufficient Condition ◽  
Lyapunov Matrix Equation ◽  
Discrete Time Systems ◽  
Lyapunov Matrix ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Contraction Theory ◽  
Time Systems

Abstract The aim of the present work is to generalize the contraction theory for the analysis of the convergence of fractional order systems for both continuous-time and discrete-time systems. Contraction theory is a methodology for assessing the stability of trajectories of a dynamical system with respect to one another. The result of this study is a generalization of the Lyapunov matrix equation and linear eigenvalue analysis. The proposed approach gives a necessary and sufficient condition for exponential and global convergence of nonlinear fractional order systems. The examples elucidate that the theory is very straightforward and exact.

scholarly journals Puu System of Fractional Order and Its Chaos Suppression

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 340 ◽  
Author(s):  
Marius-F. Danca
Keyword(s):  
Periodic Solutions ◽  
Fractional Order ◽  
Discrete Time ◽  
Continuous Time ◽  
Control Algorithm ◽  
Chaos Control ◽  
Chaos Suppression ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Order Continuous

In this paper, the fractional-order variant of Puu’s system is introduced, and, comparatively with its integer-order counterpart, some of its characteristics are presented. Next, an impulsive chaos control algorithm is applied to suppress the chaos. Because fractional-order continuous-time or discrete-time systems have not had non-constant periodic solutions, chaos suppression is considered under some numerical assumptions.

scholarly journals On the Q–S Chaos Synchronization of Fractional-Order Discrete-Time Systems: General Method and Examples

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Adel Ouannas ◽  
Amina-Aicha Khennaoui ◽  
Giuseppe Grassi ◽  
Samir Bendoukha
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Chaos Synchronization ◽  
Control Strategies ◽  
Linearization Method ◽  
Discrete Time Systems ◽  
Control Scheme ◽  
The Stability ◽  
Time Systems ◽  
General Method

In this paper, we propose two control strategies for the Q–S synchronization of fractional-order discrete-time chaotic systems. Assuming that the dimension of the response system m is higher than that of the drive system n, the first control scheme achieves n-dimensional synchronization whereas the second deals with the m-dimensional case. The stability of the proposed schemes is established by means of the linearization method. Numerical results are presented to confirm the findings of the study.

On fractional–order discrete–time systems: Chaos, stabilization and synchronization

2019 ◽  
Vol 119 ◽  
pp. 150-162 ◽  
Author(s):  
Amina-Aicha Khennaoui ◽  
Adel Ouannas ◽  
Samir Bendoukha ◽  
Giuseppe Grassi ◽  
René Pierre Lozi ◽  
...  
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Chaos Stabilization

Stability and robustness for discrete-time systems with control signal saturation

2000 ◽  
Vol 214 (1) ◽  
pp. 65-76 ◽  
Author(s):  
A R Plummer ◽  
C S Ling
Keyword(s):  
Discrete Time ◽  
Controller Design ◽  
Control Signal ◽  
Design Stage ◽  
System Control ◽  
Stability Robustness ◽  
Discrete Time Systems ◽  
The Stability ◽  
Time Systems ◽  
Signal Saturation

All practical control systems exhibit control signal saturation. The effect that this saturation has on the control system performance, especially stability and robustness, can be significant and must be understood at the controller design stage. This paper presents conditions for global asymptotic stability and measures of stability robustness for such systems. These are demonstrated through simulation examples, and it is shown how an understanding of the stability conditions can inform the controller design process. The off-axis circle criterion is used as the basis for a sufficient condition for stability, and it is argued that this is not overly restrictive in practice. The derivations are carried out in discrete time, and servo-system control is envisaged as an important application area for the techniques; however, the results are applicable more widely.

A delay-partitioning approach to the stability analysis of discrete-time systems

Automatica ◽  
2010 ◽  
Vol 46 (3) ◽  
pp. 610-614 ◽  
Author(s):  
Xiangyu Meng ◽  
James Lam ◽  
Baozhu Du ◽  
Huijun Gao
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Discrete Time Systems ◽  
The Stability ◽  
Time Systems ◽  
Delay Partitioning
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