The Stability Cone for a Matrix Delay Difference Equation
| Autor: | M. M. Kipnis, V. V. Malygina |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | International Journal of Mathematics and Mathematical Sciences, Vol 2011 (2011) |
| Druh dokumentu: | article |
| ISSN: | 0161-1712 1687-0425 |
| DOI: | 10.1155/2011/860326 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|