Modeling of Discrete-Time Fractional-Order State Space Systems Using the Balanced Truncation Method

2015 ◽  
pp. 119-127 ◽  
Author(s):  
Marek Rydel ◽  
Rafał Stanisławski ◽  
Grzegorz Bialic ◽  
Krzysztof J. Latawiec
Keyword(s):  
State Space ◽  
Fractional Order ◽  
Discrete Time ◽  
Balanced Truncation ◽  
Space Systems ◽  
Truncation Method ◽  
State Space Systems ◽  
Order State

STABILITY OF DISCRETE FRACTIONAL ORDER STATE-SPACE SYSTEMS

2006 ◽  
Vol 39 (11) ◽  
pp. 505-510 ◽  
Author(s):  
Andrzej Dzieliński ◽  
Dominik Sierociuk
Keyword(s):  
State Space ◽  
Fractional Order ◽  
Space Systems ◽  
State Space Systems ◽  
Order State

OBSERVER FOR DISCRETE FRACTIONAL ORDER STATE-SPACE SYSTEMS

2006 ◽  
Vol 39 (11) ◽  
pp. 511-516 ◽  
Author(s):  
Andrzej Dzieliński ◽  
Dominik Sierociuk
Keyword(s):  
State Space ◽  
Fractional Order ◽  
Space Systems ◽  
State Space Systems ◽  
Order State

scholarly journals Parallel Implementation of Modeling of Fractional-Order State-Space Systems Using the Fixed-Step Euler Method

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 931 ◽  
Author(s):  
Rafał Stanisławski ◽  
Kamil Kozioł
Keyword(s):  
State Space ◽  
Fractional Order ◽  
High Efficiency ◽  
Parallel Implementation ◽  
Euler Method ◽  
Processing Unit ◽  
Space Systems ◽  
Central Processing ◽  
State Space Systems ◽  
Order State

This paper presents new results in implementation of parallel computing in modeling of fractional-order state-space systems. The methods considered in the paper are based on the Euler fixed-step discretization scheme and the Grünwald-Letnikov definition of the fractional-order derivative. Two different parallelization approaches for modeling of fractional-order state-space systems are proposed, which are implemented both in Central Processing Unit (CPU)- and Graphical Processing Unit (GPU)-based hardware environments. Simulation examples show high efficiency of the introduced parallelization schemes. Execution times of the introduced methodology are significantly lower than for the classical, commonly used simulation environment.

Stability of Discrete Fractional Order State-space Systems

2008 ◽  
Vol 14 (9-10) ◽  
pp. 1543-1556 ◽  
Author(s):  
Andrzej Dzieliński ◽  
Dominik Sierociuk
Keyword(s):  
State Space ◽  
Fractional Order ◽  
Space Systems ◽  
State Space Systems ◽  
Order State

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.

New Conditions and Numerical Checking Method for the Practical Stability of Fractional Order Positive Discrete-Time Linear Systems

2019 ◽  
Vol 20 (3-4) ◽  
pp. 315-323
Author(s):  
Hongli Yang ◽  
Yuexiao Jia
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
The State ◽  
Practical Stability ◽  
Space Systems ◽  
State Matrix ◽  
Numerical Examples ◽  
State Space Systems ◽  
Linear State ◽  
Time Linear

AbstractPractical stability of a fractional order discrete-time linear state-space systems was put up in recent years. It is usually checked by the eigenvalues of the state matrix, some methods have been given during these years. But if the size of the state matrix is large, the computations of eigenvalues can be very onerous. In this paper, some new conditions on practical stability for positive fractional discrete-time linear system are presented. Numerically checking method of practical stability is presented based on the new conditions given in this paper. It is illustrated by the numerical examples that our checking method is effective and true. Compared to the now existing methods, numerically checking method is an attractive method because it’s easily implemented.

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