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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |