scholarly journals Direct discretization of the fractional-order differential by using Chebyshev series expansion

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 2020011-2020012 ◽  
Author(s):  
Tsuyako Miyakoda
Keyword(s):  
Series Expansion ◽  
Fractional Order ◽  
Chebyshev Series ◽  
Chebyshev Series Expansion

scholarly journals Observation of a Class of Disturbance in Time Series Expansion for Fractional Order Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Yiheng Wei ◽  
Hamid Reza Karimi ◽  
Jinwen Pan ◽  
Qing Gao ◽  
Yong Wang
Keyword(s):  
Time Series ◽  
Series Expansion ◽  
Fractional Order ◽  
Disturbance Observer ◽  
Higher Order ◽  
Transient Dynamics ◽  
Fractional Order Systems ◽  
Weighted Function ◽  
Numerical Examples ◽  
The Stability

This paper is concerned with the problem of designing disturbance observer for fractional order systems, of which the disturbance is in time series expansion. The stability of a special observer with the selected nonlinear weighted function and transient dynamics function is rigorously analyzed for slowly varying disturbance. In addition, the result is also extended to estimate slope forms disturbance and higher order disturbance of fractional order systems. The efficacy of the proposed method is validated through numerical examples.

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