Tytuł artykułu
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Abstrakty
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.
Czasopismo
Rocznik
Tom
Strony
37--55
Opis fizyczny
Bibliogr. 11 poz.
Twórcy
autor
autor
autor
- Department of Mathematics, University of Athens, Panepistimiopolis, 157 84 Athens, Greece, gkaloger@math.uoa.gr
Bibliografia
- [1] Antsaklis P.J., Michel A.N., Linear systems, McGraw-Hill, Inc., USA, 1997.
- [2] Ben-Israel A., Greville T.N.E., Generalized Inverses: theory and applications, John Wiley and Sons, Inc., New York, 1974.
- [3] Bjerhammar A., A generalized matrix algebra, Kungl. Tekn. Hogsk. Handl., 124, 1968, pp. 1-32.
- [4] Bowen J.M., Delta function terms arising from classical point source fields. Am. J. Phys., Vol. 62, 1994, pp. 511-515.
- [5] Datta N.B., Numerical Linear Algebra and applications, Brooks and Cole, Pacific Grove, California, USA, 1995.
- [6] Gupta S.C., Hasdort T L., Changing the state of a linear system by use of normal function and its derivatives, J. Electronics Control, Vol. 14, 1963. pp. 351-359.
- [7] Gupta S.C., Transform and slate variable methods in linear systems. Wiley, New York, USA, 1966.
- [8] Kanwal R.P., Generalized Functions: Theory and applications, Birkäuser, 3rd ed., USA, 2004.
- [9] Penrose R., A generalized inverse for matrices, Proc. Cambridge Rhilos. 51, 1955, pp. 406-413.
- [10] Roos B.W., Analytic functions and distributions in physic and engineering, Wiley, New York, USA, 1969.
- [11] Zemanian A.H., Distribution theory and transform analysis: An introduction to generalized functions, with applications, Dover Publications, Inc., New York, USA, 1987.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0033-0037