Stability by the linear approximation

  • J. P. LaSalle
Part of the Applied Mathematical Sciences book series (AMS, volume 62)


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
$$x' = Ax$$
determines the stability of the nonlinear equation,
$$x' = Ax + f\left( x \right)$$


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Copyright information

© Springer Science+Business Media New York 1986

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  • J. P. LaSalle

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