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.

scholarly journals Chaos synchronization of fractional–order discrete–time systems with different dimensions using two scaling matrices

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 942-949 ◽  
Author(s):  
Adel Ouannas ◽  
Samir Bendoukha ◽  
Amina–Aicha Khennaoui ◽  
Giuseppe Grassi ◽  
Xiong Wang ◽  
...  
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Strategies ◽  
Response System ◽  
Discrete Time Systems ◽  
Different Dimensions ◽  
Synchronization Scheme ◽  
Time Systems

Abstract In this paper, we study the synchronization of fractional–order discrete–time chaotic systems by means of two scaling matrices Θ and Φ. The considered synchronization scheme can be tailored to encompass several types of classical synchronization types. We proposed two nonlinear control strategies for the Θ–Φ synchronization of an m–dimensional drive system and an n–dimensional response system, whereby the synchronization dimension d = m and d = n, respectively. Numerical examples are presented to test the findings of the study.

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.

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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