Time-Delay Synchronization and Anti-Synchronization of Variable-Order Fractional Discrete-Time Chen–Rossler Chaotic Systems Using Variable-Order Fractional Discrete-Time PID Control

In this research paper, we solve the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional-order differential equations. To guarantee the synchronization and anti-synchronization, we use the well-known PID (Proportional-Integral-Derivative) control theory and the Lyapunov–Krasovskii stability theory for discrete systems of a variable fractional order. We illustrate the results obtained through simulation with examples, in which it can be seen that our results are satisfactory, thus achieving synchronization and anti-synchronization of chaotic systems of a variable fractional order with discrete time delay.

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Time-Delay Synchronization and anti-Synchronization of Variable-Order Fractional Discrete-Time of Chen-Rossler Chaotics Systems Using Variable-Order Fractional-Discrete Time PID Control

10.20944/preprints202108.0121.v1 ◽

2021 ◽

Author(s):

Joel Perez P. ◽

J. Javier Perez D. ◽

Jose P. Perez ◽

Atilano Martinez Huerta

Keyword(s):

Time Delay ◽

Fractional Order ◽

Discrete Time ◽

Pid Control ◽

Chaotic Systems ◽

Discrete Systems ◽

Variable Order ◽

Fractional Order Differential Equations ◽

Research Article ◽

Discrete Time Delay

In this research article we solve the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional order differential equations. To guarantee the synchronization and anti-synchronization of these systems, we use the well-known PID control theory and the Lyapunov-Krasovskii stability theory for discrete systems of variable fractional order.We illustrate the results obtained through simulation with examples, in which it can be seen that our results are satisfactory, thus achieving synchronization and anti-synchronization of chaotic systems of variable fractional order with discrete time delay.

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Input-to-state stability of discrete time-delay systems with switching and impulsive signals

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331217744617 ◽

2018 ◽

Vol 40 (15) ◽

pp. 4175-4184 ◽

Cited By ~ 5

Author(s):

Zhengbao Cao ◽

Lijun Gao ◽

Meng Zhang

Keyword(s):

Time Delay ◽

Control Systems ◽

Discrete Time ◽

Discrete Systems ◽

Network Control ◽

Delay Systems ◽

Time Delay Systems ◽

Delay Bound ◽

Discrete Time Delay ◽

Network Control Systems

This paper investigates input-to-state stability (ISS) for a class of discrete time-delay systems with switching and impulsive signals. By the Lyapunov–Krasovskii technique, a dwell-time bound and delay bound are clearly presented to contribute to the ISS for discrete time-delay systems. A significant subsequence method of the switched and impulsive sequence will firstly be applied to study the ISS of discrete systems. Based on this method, some new conditions guaranteeing ISS are presented. Compared with the existing results on related problems, the obtained stability criteria are less conservative as it is only required for the specially designed Lyapunov function to be non-increasing along each of the defined subsequences of the switched and impulsive time. Examples of network control systems are presented to illustrate the main results at the end.

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Discrete-Time Approximation of Multivariable Continuous-Time Delay Systems

Handbook of Research on Advanced Intelligent Control Engineering and Automation - Advances in Computational Intelligence and Robotics ◽

10.4018/978-1-4666-7248-2.ch019 ◽

2015 ◽

pp. 516-542 ◽

Cited By ~ 2

Author(s):

Bemri H'mida ◽

Mezlini Sahbi ◽

Soudani Dhaou

Keyword(s):

Time Delay ◽

Discrete Time ◽

Continuous Time ◽

Computational Cost ◽

Discrete Systems ◽

Delay Systems ◽

Time Delay Systems ◽

Sampled Data ◽

Discrete Time Delay ◽

Continuous Time Delay

Many works are related to the analysis and control of either continuous or else discrete time-delay systems. In general, discrete-time controls have become more and more preferable in engineering because of their easy implementation and simple computation. However, the available discretization approaches for the systems having time delays increase the system dimensions and have a high computational cost. The case studies in this chapter support the efficiency of the two methods. However, the discretization of continuous time-delay systems has not been sufficiently/extensively studied in many works. In this work, the authors present two methods of the effective discretization approach for the continuous-time systems with an input and output delays. Sampled-data time-delay systems with internal and external point delays are described by approximate discrete time-delay systems in the discrete domain. These approximate discrete systems allow the hybrid control of time-delay systems.

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