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Fractional kalman filter algorithm for the states parameters and order of fractional system estimation

100%
Sierociuk D., Dzieliński A.
International Journal of Applied Mathematics and Computer Science
|
2006
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tom 16
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nr 1
129-140
EN
This paper presents a generalization of the Kalman filter for linear and nonlinear fractional order discrete state-space systems. Linear and nonlinear discrete fractional order state-space systems are also introduced. The simplified kalman filter for the linear case is called the fractional Kalman filter and its nonlinear extension is named the extended fractional Kalman filter. The background and motivations for using such techniques are given, and some algorithms are discussed. The paper also shows a simple numerical example of linear state estimation. Finally, as an example of nonlinear estimation, the paper discusses the possibility of using these algorithms for parameters and fractional order estimation for fractional order systems. Numerical examples of the use of these algorithms in a general nonlinear case are presented.
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Controllability and observability of linear discrete-time fractional-order systems

86%
Guermah S., Djennoune S., Bettayeb M.
International Journal of Applied Mathematics and Computer Science
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2008
|
tom 18
|
nr 2
213-222
EN
In this paper we extend some basic results on the controllability and observability of linear discrete-time fractional-order systems. For both of these fundamental structural properties we establish some new concepts inherent to fractional-order systems and we develop new analytical methods for checking these properties. Numerical examples are presented to illustrate the theoretical results.
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