A Rational Approximation Method of Fractional Order Differentiators and Integrators Based On Joint Optimal Criterion

2016 ◽  
Vol 9 (6) ◽  
pp. 251-264
Author(s):  
Huimin Zhao ◽  
Chen Guo ◽  
Wu Deng ◽  
Dongyan Li ◽  
Xinhua Yang ◽  
...  
Keyword(s):  
Fractional Order ◽  
Rational Approximation ◽  
Approximation Method ◽  
Optimal Criterion

Sub-Optimum H2 Rational Approximations to Fractional Order Linear Systems

2005 ◽  
Author(s):  
Dingyu¨ Xue ◽  
YangQuan Chen
Keyword(s):  
Linear Systems ◽  
Fractional Order ◽  
Rational Approximation ◽  
Approximation Method ◽  
Linear Time ◽  
Rational Approximations ◽  
Order Linear ◽  
Integer Order ◽  
Linear Time Invariant ◽  
Time Invariant

In this paper, we propose a procedure to achieve rational approximation to arbitrary fractional order linear time invariant (FO-LTI) systems with sub-optimum H2-norm. Through illustrations, we show that the rational approximation is simple and effective. It is also demonstrated that this sub-optimum approximation method is effective in designing integer order controllers for FO-LTI systems in general form. Useful Matlab codes are also given in the appendices.

Analysis of a Nonlinear System with a Random Parameter

2014 ◽  
Vol 721 ◽  
pp. 366-369
Author(s):  
Hong Gang Dang ◽  
Xiao Ya Yang ◽  
Wan Sheng He
Keyword(s):  
Nonlinear System ◽  
Fractional Order ◽  
Approximation Method ◽  
Lorenz System ◽  
Laguerre Polynomial ◽  
Random Parameter ◽  
Order System ◽  
Order Complex ◽  
Ensemble Mean ◽  
Complex Lorenz System

In this paper, a nonlinear system with random parameter, which is called stochastic fractional-order complex Lorenz system, is investigated. The Laguerre polynomial approximation method is used to study the system. Then, the stochastic fractional-order system is reduced into the equivalent deterministic one with Laguerre approximation. The ensemble mean and sample responses of the stochastic system can be obtained.

The calculation of critical indices by the rational approximation method

1982 ◽  
Vol 15 (10) ◽  
pp. 3233-3240 ◽  
Author(s):  
R T Baumel ◽  
J L Gammel ◽  
J Nuttall ◽  
D C Power
Keyword(s):  
Rational Approximation ◽  
Approximation Method ◽  
Critical Indices

On existence and uniqueness results for iterative mixed integrodifferential equation of fractional order

2020 ◽  
Vol 26 (2) ◽  
pp. 263-272
Author(s):  
S. I. Unhale ◽  
Subhash D. Kendre
Keyword(s):  
Numerical Solution ◽  
Fractional Order ◽  
Integrodifferential Equation ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Integrodifferential Equations ◽  
Successive Approximation Method ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

AbstractThe objective of this work is to study the local existence, uniqueness, stability and other properties of solutions of iterative mixed integrodifferential equations of fractional order. The Successive Approximation Method is applied for the numerical solution of iterative mixed integrodifferential equations of fractional order.

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