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1986 | OriginalPaper | Chapter

Stability by the linear approximation

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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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 $$x' = Ax + f\left( x \right)$$

previous chapter Liapunov’s characterization of stable matrices. A Liapunov function for x’ = Ax
next chapter The general solution of x’ = Ax. The Jordan Canonical Form.
Metadata
Title
Stability by the linear approximation
Author
J. P. LaSalle
Copyright Year
1986
Publisher
Springer New York
Book
The Stability and Control of Discrete Processes

Print ISBN: 978-0-387-96411-9

Electronic ISBN: 978-1-4612-1076-4

Copyright Year: 1986

DOI
https://doi.org/10.1007/978-1-4612-1076-4_7