Liapunov Function

I googled "the appropriate Lyapunov function for an ODE lecture" and checked till page 2.

Here are some interesting links:

http://mechatronics.ece.usu.edu/ece7360/notes/7360w1a_overview_linear_algebra.pdf
http://www.ma.hw.ac.uk/~takis/probcourse06/notes/SS_LYAPUNOV.pdf
https://www.cds.caltech.edu/help/uploads/wiki/files/204/Lectures1-2_CDS270.pdf
https://www.cds.caltech.edu/help/uploads/wiki/files/178/Lecture1.pdf
http://www.nd.edu/~lemmon/courses/ee580/lecture-6.pdf