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The use of impulse-function and its derivatives for changing the state of a multi-input multi-output differential system in (almost) zero time

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Kalogeropoulos G. I. , Karageorgos A. D. , Pantelous A. A.

Systems Science

2008

tom Vol. 34, no 3

11-15

In many practical applications, the (almost) zero time state changing is more than important. Thus, in this short paper we develop a methodology for the state changing of a multi-input multi-output linear control differential system by using a linear combination of Dirac δ-function and its derivatives. Obviously, such an input is very hard to imagine physically. Using linear algebra techniques and the generalized inverse theory, the input's coefficients are fully determined. Finally, the whole work ends up with the analytic presentation of an illustrative numerical example.

Changing the state of a linear differential system in (almost) zero time by using distributional input function

100%

Kalogeropoulos G. I. , Karageorgos A. D. , Pantelous A. A.

Systems Science

2007

tom Vol. 33, no 4

37-55

In many physical (for instance, in thermodynamics) or in more economic dynamic systems the (almost) zero - time state changing is more than important. One of the most typical state changing in (almost) zero time is appeared whenever the financial institution managers are predetermined the interest rate policy. Thus, in this paper we investigate the state changing of a linear differential system in (almost) zero time by using a linear combination of Dirac δ-function and its derivatives. Obviously, such an input is very hard to imagine physically. However, we can think of it approximately as a combination of small pulses of very high magnitude and infinitely small duration. Using linear algebra techniques and the generalized inverse theory, the input's coefficients are fully determined. Finally, the whole paper ends up with the analytic presentation of an illustrative numerical example.

On the perturbation of linear regular descriptor systems

100%

Kalogeropoulos G. I. , Karageorgos A. D. , Pantelous A. A.

Systems Science

2009

tom Vol. 35, no 4

5-13

In the perturbation theory of linear descriptor systems, it is well known that the theory of eigenvalues and eigenvectors of regular homogeneous matrix pencils is complicated by the fact that arbitrarily small perturbations of the pencil can cause them to disappear. In this paper, the perturbation theory of complex Weierstrass canonical form for regular matrix pencils is investigated. Moreover, since there are applications such that the eigenvalues and eigenvectors do not disappear upon by arbitrarily small perturbations, expressions for the relative error of Fw and Gw, i.e., [wzór] are provided by using the Frobenius norm [wzór].