https://murray.cds.caltech.edu/index.php?title=What_is_the_significance_of_having_eigenvalues_that_are_0%3F_I_think_I_heard_you_say_%22in_that_case_you_don%27t_know_anything%22._Does_that_mean_you_cannot_determine_if_the_system_is_stable_or_asymptotically_stable%3F&feed=atom&action=historyWhat is the significance of having eigenvalues that are 0? I think I heard you say "in that case you don't know anything". Does that mean you cannot determine if the system is stable or asymptotically stable? - Revision history2021-10-22T06:18:57ZRevision history for this page on the wikiMediaWiki 1.35.3https://murray.cds.caltech.edu/index.php?title=What_is_the_significance_of_having_eigenvalues_that_are_0%3F_I_think_I_heard_you_say_%22in_that_case_you_don%27t_know_anything%22._Does_that_mean_you_cannot_determine_if_the_system_is_stable_or_asymptotically_stable%3F&diff=8139&oldid=prevHan at 23:37, 6 October 20082008-10-06T23:37:37Z<p></p>
<p><b>New page</b></p><div>In today's lecture we were trying to analyze (rather than design) the stability of a given system, so the eigenvalues are already fixed. In the case that one or more eigenvalues are zero, you can say the following things depending on the type of system:<br />
<br />
* Linear system, can be transformed into diagonal form (4.8):<br />
System is stable (in the sense of Lyapunov) if all other eigenvalues are strictly negative.<br />
<br />
* Linear system, can be transformed into the block diagonal form on page 106:<br />
System is stable (in the sense of Lyapunov) if the real parts all other eigenvalues are strictly negative.<br />
<br />
* Linear system, cannot be transformed into the above two forms:<br />
In general cannot determine the stability. <br />
<br />
* Linearized version of a nonlinear system: <br />
In general cannot determine the stability.<br />
<br />
--Shuo<br />
<br />
[[Category: CDS 101/110 FAQ - Lecture 2-1]]<br />
[[Category: CDS 101/110 FAQ - Lecture 2-1, Fall 2008]]</div>Han