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Erschienen in:
1986 | OriginalPaper | Buchkapitel
Stability by the linear approximation
verfasst von : J. P. LaSalle
Erschienen in: The Stability and Control of Discrete Processes
Verlag: Springer New York
Enthalten in: Professional Book Archive
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The oldest method of investigating the stability of a system is to replace the system by its linear approximation. This method was used long before Liapunov, although Liapunov appears to be the first person who justified the method for ordinary differential equations. In 1929 Perron [1] investigated the question of when the stability of the difference equation 7.1 $$x' = Ax$$ determines the stability of the nonlinear equation,7.2 $$x' = Ax + f\left( x \right)$$