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A strategy for constructing Lyapunov functions for non-autonomous linear differential equations

✍ Scribed by C. Connell McCluskey

Publisher: Elsevier Science
Year: 2005
Tongue: English
Weight: 225 KB
Volume: 409
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2005.04.006

No coin nor oath required. For personal study only.

✦ Synopsis

A strategy is presented for determining if the growth of solutions to a non-autonomous linear differential equation satisfies a given bound. In the case where the given bound is negative, the approach gives a constructive method for finding a Lyapunov function and showing that the system is stable. The strategy takes advantage of the sign pattern of the coefficient matrix and is demonstrated with an example.

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