scholarly journals State Estimation of Continuous-Time Linear Fractional-Order Systems Disturbed by Correlated Colored Noises via Tustin Generating Function

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 18362-18373 ◽  
Author(s):  
Xiaomin Huang ◽  
Zhe Gao ◽  
Chao Yang ◽  
Fanghui Liu
Keyword(s):  
State Estimation ◽  
Fractional Order ◽  
Generating Function ◽  
Continuous Time ◽  
Fractional Order Systems ◽  
Time Linear

scholarly journals Design of unknown input fractional-order observers for fractional-order systems

2013 ◽  
Vol 23 (3) ◽  
pp. 491-500 ◽  
Author(s):  
Ibrahima N’Doye ◽  
Mohamed Darouach ◽  
Holger Voos ◽  
Michel Zasadzinski
Keyword(s):  
Fractional Order ◽  
Continuous Time ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Fractional Order Systems ◽  
Matrix Inequalities ◽  
Order Error ◽  
Error System ◽  
Time Linear

Abstract This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach, where the fractional order α belongs to 1≤α<2 and 0<α≤1, respectively. A stability analysis of the fractional-order error system is made and it is shown that the fractional-order observers are as stable as their integer order counterpart and guarantee better convergence of the estimation error.

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.

On Observability and Pseudo State Estimation of Fractional Order Systems

2012 ◽  
Vol 18 (3) ◽  
pp. 260-271 ◽  
Author(s):  
Jocelyn Sabatier ◽  
Christophe Farges ◽  
Mathieu Merveillaut ◽  
Ludovic Feneteau
Keyword(s):  
State Estimation ◽  
Fractional Order ◽  
Fractional Order Systems

State estimation for nonlinear conformable fractional‐order systems: A healthy operating case and a faulty operating case

2019 ◽  
Vol 22 (5) ◽  
pp. 1870-1879 ◽  
Author(s):  
Assaad Jmal ◽  
Mourad Elloumi ◽  
Omar Naifar ◽  
Abdellatif Ben Makhlouf ◽  
Mohamed Ali Hammami
Keyword(s):  
State Estimation ◽  
Fractional Order ◽  
Fractional Order Systems
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