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An observability problem for a class of uncertain-parameter linear dynamic systems

100%
Oprzędkiewicz K.
International Journal of Applied Mathematics and Computer Science
|
2005
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tom 15
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nr 3
331-338
EN
An observability problem for a class of linear, uncertain-parameter, time-invariant dynamic SISO systems is discussed. The class of systems under consideration is described by a finite dimensional state-space equation with an interval diagonal state matrix, known control and output matrices and a two-dimensional uncertain parameter space. For the system considered a simple geometric interpretation of the system spectrum can be given. The geometric interpretation of the system spectrum is the base for defining observability and non-observability areas for the discussed system. The duality principle allows us to test observablity using controllability criteria. For the uncertain-parameter system considered, some controllability criteria presented in the author's previous papers are used. The results are illustrated with numerical examples.
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Modeling heat distribution with the use of a non-integer order, state space model

51%
Oprzędkiewicz K., Gawin E., Mitkowski W.
International Journal of Applied Mathematics and Computer Science
|
2016
|
tom 26
|
nr 4
749-756
EN
A new, state space, non-integer order model for the heat transfer process is presented. The proposed model is based on a Feller semigroup one, the derivative with respect to time is expressed by the non-integer order Caputo operator, and the derivative with respect to length is described by the non-integer order Riesz operator. Elementary properties of the state operator are proven and a formula for the step response of the system is also given. The proposed model is applied to the modeling of temperature distribution in a one dimensional plant. Results of experiments show that the proposed model is more accurate than the analogical integer order model in the sense of the MSE cost function.
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