scholarly journals Bounded real lemma for singular linear continuous-time fractional-order systems

Automatica ◽  
2022 ◽  
Vol 135 ◽  
pp. 109962
Author(s):  
Saliha Marir ◽  
Mohammed Chadli ◽  
Michael V. Basin
Keyword(s):  
Fractional Order ◽  
Continuous Time ◽  
Fractional Order Systems ◽  
Bounded Real Lemma

Fractional-order Kalman filters for continuous-time fractional-order systems involving correlated and uncorrelated process and measurement noises

2018 ◽  
Vol 41 (7) ◽  
pp. 1933-1947 ◽  
Author(s):  
Fanghui Liu ◽  
Zhe Gao ◽  
Chao Yang ◽  
Ruicheng Ma
Keyword(s):  
Fractional Order ◽  
Continuous Time ◽  
Kalman Filters ◽  
Equation Model ◽  
Order System ◽  
Fractional Order Systems ◽  
Derivative Method ◽  
Measurement Noises ◽  
Computation Load ◽  
Average Derivative

This paper presents fractional-order Kalman filters using the fractional-order average derivative method for linear fractional-order systems involving process and measurement noises. By using the fractional-order average derivative method, a difference equation model is obtained by discretizing the investigated continuous-time fractional-order system, and the accuracy of state estimation is improved. Meanwhile, compared with the Tustin generating function, the fractional-order average derivative method proposed in this paper can reduce computation load and save calculation time. Two kinds of fractional-order Kalman filters are given, for the correlated and uncorrelated cases, in terms of the process and measurement noises for linear fractional-order systems, respectively. Finally, simulation results are illustrated to verify the effectiveness of the proposed Kalman filters using the fractional-order average derivative method.

scholarly journals Recursive system identification for coefficient estimation of continuous-time fractional order systems

2021 ◽  
Vol 54 (7) ◽  
pp. 114-119
Author(s):  
Jean-François Duhé ◽  
Stéphane Victor ◽  
Pierre Melchior ◽  
Youssef Abdelmounen ◽  
François Roubertie
Keyword(s):  
System Identification ◽  
Fractional Order ◽  
Continuous Time ◽  
Fractional Order Systems ◽  
Coefficient Estimation ◽  
Recursive System
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