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

Parameter Identification of Fractional Order Systems Using a Collocation Method Based on Hybrid Functions

2020 ◽  
Vol 142 (8) ◽  
Author(s):  
Y. Lu ◽  
J. Zhang ◽  
Y. G. Tang
Keyword(s):  
Integral Operator ◽  
Collocation Method ◽  
Fractional Order ◽  
Analytical Form ◽  
Fractional Order Systems ◽  
Actual System ◽  
Hybrid Functions ◽  
Block Pulse Functions ◽  
The Laplace Transform ◽  
Fractional Order Integral

Abstract In this paper, we propose a novel collocation method based on hybrid functions to identify the parameters and differential orders of fractional order systems (FOS). The hybrid functions consist of block-pulse functions and Taylor polynomials. The analytical form of Riemann–Liouville fractional order integral operator of these hybrid functions is derived using the Laplace transform. Then the integral operator is utilized, in conjunction with collocation points, to convert the FOS into an algebraic system directly. The parameters and differential orders of the FOS are estimated by minimizing the error between the output of the actual system and that of the estimated system. The effectiveness of the proposed method is verified through four examples.

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.

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