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 |
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Hindawi Limited
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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doaj-5875dc8cb06d49158d3fd0414babace82020-11-24T22:27:20ZengHindawi LimitedInternational 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
M. M. Kipnis V. V. Malygina |
| spellingShingle |
M. M. Kipnis V. V. Malygina The Stability Cone for a Matrix Delay Difference Equation International Journal of Mathematics and Mathematical Sciences |
| author_facet |
M. M. Kipnis V. V. Malygina |
| author_sort |
M. M. Kipnis |
| title |
The Stability Cone for a Matrix Delay Difference Equation |
| title_short |
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_sort |
stability cone for a matrix delay difference equation |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2011-01-01 |
| 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. |
| 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 |
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1725750401038286848 |