Liapunov functions I would really like to see some very simple worked out or with some well pointed hints on these guys. i have two textbooks that outline the idea behind them, but both give only one example that are very contribbed imho. ( Non-Linear dynamics and intro to chaos By Steven H Strogatz) and (differential equations, dynamical systems and intro to chaos by Morris W. Hirsch.) Textbook or links to instructive material on this subject much appreciated. ( im an ungrad and not from math so please don't bludgeon me to death thx.)

Note: Be careful that the name is spelled two different ways "Liapunov" or "Lyapunov", so when searching, try both!

These papers might be instructive:

* _Lyapunov function methods_
* _MIT Lectures on Dynamic Systems and Control_
* _MIT - Finding Lyapunov Functions_
* _A comparison of three methods of constructing Lyapunov functions_
* _Stability theory for systems of dierential equations with applications to power control in wireless networks_



**Books** These have a handful of pages each and I like the first two most.

* Modern Control Theory, W. Brogan (very nice write-up on the matter, with physical and electrical circuits)
* The Qualitative Theory of Ordinary Differential Equations, An Introduction, F. Brauer and J.A. Nohel
* Ordinary Differential Equations, V.I. Arnold
* Dynamics and Bifurcations, J. Hale and H Kocak
* Nonlinear systems, H.K. Khalil



There may be some applied materials from Physics areas that might also help.