Reachability and Holdability of Nonnegative States
| Autor: | Michael J. Tsatsomeros, D. Noutsos |
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| Rok vydání: | 2008 |
| Předmět: | |
| Zdroj: | SIAM Journal on Matrix Analysis and Applications. 30:700-712 |
| ISSN: | 1095-7162 0895-4798 |
| DOI: | 10.1137/070693850 |
| Popis: | Linear differential systems $\dot{x}(t)=Ax(t)$ ($A\in\mathbb{R}^{n\times n}$, $x_0=x(0)\in\mathbb{R}^n$, $t\geq0$) whose solutions become and remain nonnegative are studied. It is shown that the eigenvalue of $A$ furthest to the right must be real and must possess nonnegative right and left eigenvectors. Moreover, for some $a\geq0$, $A+aI$ must be eventually nonnegative, that is, its powers must become and remain entrywise nonnegative. Initial conditions $x_0$ that result in nonnegative states $x(t)$ in finite time are shown to form a convex cone that is related to the matrix exponential $e^{tA}$ and its eventual nonnegativity. |
| Databáze: | OpenAIRE |
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