Wyniki wyszukiwania - Biblioteka Nauki

1

A class of LTI descriptor (regular) differential systems with distributed continuous delays and several types of inputs

100%

Pantelous A. A. , Kalogeropoulos G. I.

|

tom Vol. 35, no 1

31-38

EN

In this paper, we consider a class of Linear Time-Invariant (LTI) descriptor (regular) differential systems with distributed continuous delays and several types of (regular and irregular) inputs. This special class of differential systems are inherent in many real-life applications; we merely mention fluid dynamics, the modelling of multi-body mechanisms, the pricing procedure of actuarial portfolios of products and the problem of protein folding. By using some elements of matrix pencil theory, we decompose the main system into two subsystems (which are so-called fast and slow systems), whose solutions are obtained as generalized processes (in the sense of the Dirac delta distributions). Moreover, the form of the initial function is given, so the corresponding initial value problem is uniquely solvable. Finally, an illustrative application inspired by Insurance is briefly presented using standard Brownian motions.

2

Pole assignment for higher order linear systems: an algorithmic method

100%

Kalogeropoulos G. I. , Papachristopoulos D. P.

Systems Science

|

2005

|

tom Vol. 31, no 4

5-20

EN

In this paper, we propose an algorithmic method for a solution of the pole assignment problem which is associated with a higher order linear system, in the case it is completely controllable. The above problem is proved to be equivalent to two subproblems, one linear and the other multilinear. Solutions of the linear problem must be decomposable vectors, that is, they lie in an appropriate Grassmann variety. The method proposed computes a reduced set of quadratic Plucker relations with only three terms each, which describe completely the specific Grassmann variety. Using these relations one can solve the multilinear problem and consequently calculate the feedback matrices which give a solution to the pole assignment problem. Finally, an illustrative example of the algorithmic procedure proposed is given.

3

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

80%

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

Systems Science

|

2007

|

tom Vol. 33, no 4

37-55

EN

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.

4

Generalized regular differential systems with distributed delay

80%

Kalogeropoulos G. I. , Kossak O. , Pantelous A. A.

Systems Science

|

2008

|

tom Vol. 34, no 1

15-22

EN

In this paper, a special class of generalized regular differential delay systems with constant coefficients is extensively studied. In practice, these kinds of systems can model the size of a population or the value of an investment. By considering the regular Matrix Pencil approach we finally decompose it into two subsystems, whose solutions are obtained. Moreover, since the initial function is given, the corresponding initial value problem is uniquely solvable. Finally, an illustrative application is presented using dde23 MatLab (m-) file based on the explicit Runge-Kutta method.

5

On the perturbation of linear regular descriptor systems

80%

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

Systems Science

|

2009

|

tom Vol. 35, no 4

5-13

EN

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].