Robust stabilizing regions of fractional-order PIλ controllers for fractional-order systems with time-delays

2015 ◽  
Vol 14 (3) ◽  
pp. 340-349 ◽  
Author(s):  
Zhe Gao ◽  
Li-Rong Zhai ◽  
Yan-Dong Liu
Keyword(s):  
Fractional Order ◽  
Time Delays ◽  
Fractional Order Systems

scholarly journals Multi-Switching Combination Synchronization of Three Fractional-Order Delayed Systems

2019 ◽  
Vol 9 (20) ◽  
pp. 4348 ◽  
Author(s):  
Bo Li ◽  
Yun Wang ◽  
Xiaobing Zhou
Keyword(s):  
Theoretical Analysis ◽  
Fractional Order ◽  
Stability Theory ◽  
Time Delays ◽  
Multiple Time ◽  
Fractional Order Systems ◽  
Delayed Systems ◽  
Combination Synchronization ◽  
Multiple Time Delays ◽  
The Stability

Multi-switching combination synchronization of three fractional-order delayed systems is investigated. This is a generalization of previous multi-switching combination synchronization of fractional-order systems by introducing time-delays. Based on the stability theory of linear fractional-order systems with multiple time-delays, we propose appropriate controllers to obtain multi-switching combination synchronization of three non-identical fractional-order delayed systems. In addition, the results of our numerical simulations show that they are in accordance with the theoretical analysis.

scholarly journals Combination Synchronization of Three Different Fractional-Order Delayed Chaotic Systems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Bo Li ◽  
Xiaobing Zhou ◽  
Yun Wang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Time Delays ◽  
Chaotic Systems ◽  
Multiple Time ◽  
Engineering Systems ◽  
Fractional Order Systems ◽  
Combination Synchronization ◽  
Multiple Time Delays ◽  
Practical Engineering

Time delay is a frequently encountered phenomenon in some practical engineering systems and introducing time delay into a system can enrich its dynamic characteristics. There has been a plenty of interesting results on fractional-order chaotic systems or integer-order delayed chaotic systems, but the problem of synchronization of fractional-order chaotic systems with time delays is in the primary stage. Combination synchronization of three different fractional-order delayed chaotic systems is investigated in this paper. It is an extension of combination synchronization of delayed chaotic systems or combination synchronization of fractional-order chaotic systems. With the help of stability theory of linear fractional-order systems with multiple time delays, we design controllers to achieve combination synchronization of three different fractional-order delayed chaotic systems. In addition, numerical simulations have been performed to demonstrate and verify the theoretical analysis.

Identification of fractional-order systems with time delays using block pulse functions

2017 ◽  
Vol 91 ◽  
pp. 382-394 ◽  
Author(s):  
Yinggan Tang ◽  
Ning Li ◽  
Minmin Liu ◽  
Yao Lu ◽  
Weiwei Wang
Keyword(s):  
Fractional Order ◽  
Time Delays ◽  
Fractional Order Systems ◽  
Block Pulse Functions

scholarly journals PID controller design for fractional-order systems with time delays

2012 ◽  
Vol 61 (1) ◽  
pp. 18-23 ◽  
Author(s):  
Hitay Özbay ◽  
Catherine Bonnet ◽  
André Ricardo Fioravanti
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Time Delays ◽  
Controller Design ◽  
Fractional Order Systems ◽  
Pid Controller Design
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