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Published in:
1986 | OriginalPaper | Chapter
A characterization of stable matrices. Computational criteria
Author : J. P. LaSalle
Published in: The Stability and Control of Discrete Processes
Publisher: Springer New York
Included in: Professional Book Archive
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We saw earlier in Section 3 that r(A) < 1 was a necessary condition for A to be stable. We now want to see that this condition is also sufficient and will prove this using the algorithm of the previous section. We give first an inductive and elementary proof, and then look at another proof that is more sophisticated and teaches us something about nonnegative matrices, which arise in and are important for many applications.