The Stability Cone for a Matrix Delay Difference Equation
We construct a stability cone, which allows us to analyze the stability of the matrix delay difference equation 𝑥𝑛=𝐴𝑥𝑛−1+𝐵𝑥𝑛−𝑘. We assume that 𝐴 and 𝐵 are 𝑚×𝑚 simultaneously triangularizable matrices. We construct 𝑚 points in ℝ3 which are functions of eigenvalues of matrices 𝐴, 𝐵 such that the equa...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/860326 |
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| author | M. M. Kipnis V. V. Malygina |
| author_facet | M. M. Kipnis V. V. Malygina |
| author_sort | M. M. Kipnis |
| collection | DOAJ |
| description | We construct a stability cone, which allows us to analyze the stability of the
matrix delay difference equation 𝑥𝑛=𝐴𝑥𝑛−1+𝐵𝑥𝑛−𝑘. We assume that 𝐴 and 𝐵 are
𝑚×𝑚 simultaneously triangularizable matrices. We construct 𝑚 points in ℝ3 which are
functions of eigenvalues of matrices 𝐴, 𝐵 such that the equation is asymptotically stable
if and only if all the points lie inside the stability cone. |
| format | Article |
| id | doaj-art-5875dc8cb06d49158d3fd0414babace8 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-5875dc8cb06d49158d3fd0414babace82025-02-03T01:29:02ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/860326860326The Stability Cone for a Matrix Delay Difference EquationM. M. Kipnis0V. V. Malygina1Department of Mathematics, South Ural State University, Chelyabinsk 454080, RussiaDepartment of Applied Mathematics and Mechanics, Perm State Technical University, Perm 614990, RussiaWe construct a stability cone, which allows us to analyze the stability of the matrix delay difference equation 𝑥𝑛=𝐴𝑥𝑛−1+𝐵𝑥𝑛−𝑘. We assume that 𝐴 and 𝐵 are 𝑚×𝑚 simultaneously triangularizable matrices. We construct 𝑚 points in ℝ3 which are functions of eigenvalues of matrices 𝐴, 𝐵 such that the equation is asymptotically stable if and only if all the points lie inside the stability cone.http://dx.doi.org/10.1155/2011/860326 |
| spellingShingle | M. M. Kipnis V. V. Malygina The Stability Cone for a Matrix Delay Difference Equation International Journal of Mathematics and Mathematical Sciences |
| title | The Stability Cone for a Matrix Delay Difference Equation |
| title_full | The Stability Cone for a Matrix Delay Difference Equation |
| title_fullStr | The Stability Cone for a Matrix Delay Difference Equation |
| title_full_unstemmed | The Stability Cone for a Matrix Delay Difference Equation |
| title_short | The Stability Cone for a Matrix Delay Difference Equation |
| title_sort | stability cone for a matrix delay difference equation |
| url | http://dx.doi.org/10.1155/2011/860326 |
| work_keys_str_mv | AT mmkipnis thestabilityconeforamatrixdelaydifferenceequation AT vvmalygina thestabilityconeforamatrixdelaydifferenceequation AT mmkipnis stabilityconeforamatrixdelaydifferenceequation AT vvmalygina stabilityconeforamatrixdelaydifferenceequation |