7. State space modelling and analysis of linear fractional-order systems

2017 ◽  
pp. 221-242
Keyword(s):  
State Space ◽  
Fractional Order ◽  
Fractional Order Systems

State-space analysis of linear fractional-order systems

2008 ◽  
Vol 42 (6-8) ◽  
pp. 825-838 ◽  
Author(s):  
Saïd Guermah ◽  
Saïd Djennoune ◽  
Maâmar Bettayeb
Keyword(s):  
State Space ◽  
Fractional Order ◽  
Fractional Order Systems ◽  
Space Analysis ◽  
State Space Analysis

scholarly journals Bayesian Inference in Non-Markovian State-Space Models With Applications to Battery Fractional-Order Systems

2018 ◽  
Vol 26 (2) ◽  
pp. 497-506 ◽  
Author(s):  
Pierre E. Jacob ◽  
Seyed Mohammad Mahdi Alavi ◽  
Adam Mahdi ◽  
Stephen J. Payne ◽  
David A. Howey
Keyword(s):  
Bayesian Inference ◽  
State Space ◽  
Fractional Order ◽  
State Space Models ◽  
Fractional Order Systems

State space realization of fractional order systems

2009 ◽  
Author(s):  
T. Djamah ◽  
R. Mansouri ◽  
M. Bettayeb ◽  
S. Djennoune ◽  
Lotfi Beji ◽  
...  
Keyword(s):  
State Space ◽  
Fractional Order ◽  
Fractional Order Systems ◽  
State Space Realization ◽  
Space Realization

On Observability of Fractional Order Systems

2009 ◽  
Author(s):  
Jocelyn Sabatier ◽  
Mathieu Merveillaut ◽  
Ludovic Fenetau ◽  
Alain Oustaloup
Keyword(s):  
Parabolic Equation ◽  
State Space ◽  
Fractional Order ◽  
The State ◽  
Fractional Order System ◽  
Order System ◽  
Fractional Order Systems ◽  
System State ◽  
Fractional Systems ◽  
Real State

In this paper, fractional order system observability is discussed. A representation of these systems that involves a classical linear integer system and a system described by a parabolic equation is used to define the system real state and to conclude that the system state cannot be observed. However, it is also shown that the state space like representation usually encountered in the literature for fractional systems, can be used to design Luenberger like observers that permit an estimation of important variables in the system.

State estimation in fractional-order systems with coloured measurement noise

2017 ◽  
Vol 40 (6) ◽  
pp. 1819-1835 ◽  
Author(s):  
Behrouz Safarinejadian ◽  
Nasrin Kianpour ◽  
Mojtaba Asad
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Fractional Order ◽  
Estimation Error ◽  
Measurement Noise ◽  
Space Systems ◽  
Fractional Order Systems ◽  
State Space Systems ◽  
Simulation Results ◽  
Order State

This paper presents new estimation methods for discrete fractional-order state-space systems with coloured measurement noise. A novel approach is proposed to convert a fractional system with coloured measurement noise to a system with white measurement noise in which the process and measurement noises are correlated with each other. In this paper, two new Kalman filter algorithms for fractional-order linear state-space systems with coloured measurement noise, as well as a new extended Kalman filter algorithm for state estimation in nonlinear fractional-order state-space systems with coloured measurement noise, are proposed. The accuracy of the equations and relations is confirmed in several theorems. The validity and effectiveness of the proposed algorithms are verified by simulation results and compared with previous work. Results show that for linear and nonlinear fractional-order systems with coloured noise, the proposed methods are more accurate than conventional methods regarding estimation error and estimation error covariance. Simulation results demonstrate that the proposed algorithms can accurately perform estimation in fractional-order systems with coloured measurement noise.

Heat transfer modeling and identification using fractional order state space models

2008 ◽  
Vol 42 (6-8) ◽  
pp. 939-951 ◽  
Author(s):  
Tounsia Jamah ◽  
Rachid Mansouri ◽  
Saïd Djennoune ◽  
Maâmar Bettayeb
Keyword(s):  
Heat Transfer ◽  
State Space ◽  
Fractional Order ◽  
State Space Models ◽  
Heat Transfer Modeling ◽  
Order State

GENERALIZED THEORY OF MAGNETO-THERMO-VISCOELASTIC SPHERICAL CAVITY PROBLEM UNDER FRACTIONAL ORDER DERIVATIVE: STATE SPACE APPROACH

2020 ◽  
Vol 9 (11) ◽  
pp. 9769-9780
Author(s):  
S.G. Khavale ◽  
K.R. Gaikwad
Keyword(s):  
State Space ◽  
Fractional Order ◽  
Order Derivative ◽  
Laplace Inversion ◽  
State Space Approach ◽  
Spherical Region ◽  
Fractional Order Derivative ◽  
Numerical Laplace Inversion ◽  
Mathcad Software ◽  
Space Approach

This paper is dealing the modified Ohm's law with the temperature gradient of generalized theory of magneto-thermo-viscoelastic for a thermally, isotropic and electrically infinite material with a spherical region using fractional order derivative. The general solution obtained from Laplace transform, numerical Laplace inversion and state space approach. The temperature, displacement and stresses are obtained and represented graphically with the help of Mathcad software.

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