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 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

scholarly journals Analysis and comparison of the stability of discrete-time and continuous-time linear systems

2016 ◽  
Vol 26 (4) ◽  
pp. 551-563
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Continuous Time ◽  
Asymptotically Stable ◽  
Discrete Time Systems ◽  
Continuous Time Systems ◽  
The Matrix ◽  
Discretization Step ◽  
Time Systems ◽  
Time Linear

Abstract The asymptotic stability of discrete-time and continuous-time linear systems described by the equations xi+1 = Ākxi and x(t) = Akx(t) for k being integers and rational numbers is addressed. Necessary and sufficient conditions for the asymptotic stability of the systems are established. It is shown that: 1) the asymptotic stability of discrete-time systems depends only on the modules of the eigenvalues of matrix Āk and of the continuous-time systems depends only on phases of the eigenvalues of the matrix Ak, 2) the discrete-time systems are asymptotically stable for all admissible values of the discretization step if and only if the continuous-time systems are asymptotically stable, 3) the upper bound of the discretization step depends on the eigenvalues of the matrix A.

Discrete-time approximationsfor continuous-time Markoviancontrol systems

1984 ◽  
Vol 16 (1) ◽  
pp. 15-16
Author(s):  
A. Hordijk ◽  
F. A. Van Der Duyn Schouten
Keyword(s):  
Decision Theory ◽  
Discrete Time ◽  
Continuous Time ◽  
Time System ◽  
Time Approximation ◽  
Discrete Time Systems ◽  
Discrete Time Approximation ◽  
And Control ◽  
Time Systems ◽  
Continuous Time System

The method of discrete-time approximation is widespread in control and decision theory. However, little attention has been paid to the conditions on parameters and control under which the discrete-time systems come close to the continuous-time system.

scholarly journals Absolute stability of a class of fractional positive nonlinear systems

2019 ◽  
Vol 29 (1) ◽  
pp. 93-98 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Absolute Stability ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Discrete Time Systems ◽  
The Absolute ◽  
Necessary And Sufficient ◽  
Time Systems

Abstract The positivity and absolute stability of a class of fractional nonlinear continuous-time and discrete-time systems are addressed. Necessary and sufficient conditions for the positivity of this class of nonlinear systems are established. Sufficient conditions for the absolute stability of this class of fractional positive nonlinear systems are also given.

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