Here are a couple of standard textbooks that have lots of examples of Lyapunov functions. These are available in the Caltech library (but not on reserve). If you have problems finding them, send me e-mail and I'll give you a copy of the relevant sections:
H. K. Khalil, Nonlinear Systems, Third Edition. Prentice-Hall, 2002. Section 4.1, pages 112-126.
M. Vidyasagar, Nonlinear Systems Analysis, Second Edition. Prentice-Hall, 1993. Section 5.3, pages 157-193.