Representation of the Solutions of Linear Discrete Systems with Constant Coefficients and Two Delays
The purpose of this paper is to develop a method for the construction of solutions to initial problems of linear discrete systems with constant coefficients and with two delays Δx(k)=Bx(k-m)+Cx(k-n)+f(k), where m,n∈ℕ, m≠n, are fixed, k=0,…,∞, B=(bij), C=(cij) are constant r×r matrices, f is a given...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/320476 |
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| author | Josef Diblík Blanka Morávková |
| author_facet | Josef Diblík Blanka Morávková |
| author_sort | Josef Diblík |
| collection | DOAJ |
| description | The purpose of this paper is to develop a method for the construction of solutions to initial problems of linear discrete systems with constant coefficients and with two delays Δx(k)=Bx(k-m)+Cx(k-n)+f(k), where m,n∈ℕ, m≠n, are fixed, k=0,…,∞, B=(bij), C=(cij) are constant r×r matrices, f is a given r×1 vector, and x is an r×1 unknown vector. Solutions are expressed with the aid of a special function called the discrete matrix delayed exponential for two delays. Such approach results in a possibility to express an initial Cauchy problem in a closed form. Examples are shown illustrating the results obtained. |
| format | Article |
| id | doaj-art-607cd16dddbb4138b3bcdea8d74d63a4 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-607cd16dddbb4138b3bcdea8d74d63a42025-08-20T03:34:48ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/320476320476Representation of the Solutions of Linear Discrete Systems with Constant Coefficients and Two DelaysJosef Diblík0Blanka Morávková1Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, 602 00 Brno, Czech RepublicDepartment of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, 602 00 Brno, Czech RepublicThe purpose of this paper is to develop a method for the construction of solutions to initial problems of linear discrete systems with constant coefficients and with two delays Δx(k)=Bx(k-m)+Cx(k-n)+f(k), where m,n∈ℕ, m≠n, are fixed, k=0,…,∞, B=(bij), C=(cij) are constant r×r matrices, f is a given r×1 vector, and x is an r×1 unknown vector. Solutions are expressed with the aid of a special function called the discrete matrix delayed exponential for two delays. Such approach results in a possibility to express an initial Cauchy problem in a closed form. Examples are shown illustrating the results obtained.http://dx.doi.org/10.1155/2014/320476 |
| spellingShingle | Josef Diblík Blanka Morávková Representation of the Solutions of Linear Discrete Systems with Constant Coefficients and Two Delays Abstract and Applied Analysis |
| title | Representation of the Solutions of Linear Discrete Systems with Constant Coefficients and Two Delays |
| title_full | Representation of the Solutions of Linear Discrete Systems with Constant Coefficients and Two Delays |
| title_fullStr | Representation of the Solutions of Linear Discrete Systems with Constant Coefficients and Two Delays |
| title_full_unstemmed | Representation of the Solutions of Linear Discrete Systems with Constant Coefficients and Two Delays |
| title_short | Representation of the Solutions of Linear Discrete Systems with Constant Coefficients and Two Delays |
| title_sort | representation of the solutions of linear discrete systems with constant coefficients and two delays |
| url | http://dx.doi.org/10.1155/2014/320476 |
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