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Published in:
1986 | OriginalPaper | Chapter
Liapunov’s characterization of stable matrices. A Liapunov function for x’ = Ax
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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Although Liapunov did not consider difference equations, what we do here is the exact analog of what Liapunov did for linear differential equations. In the context of differential equations a matrix is said to be stable if $${e^{At}} \to 0$$ as $$t \to \infty $$ , and for difference equations An is the analog of eAt.