Using matlab to solve Lyapunov function

Consider the following system

dx/dt=z
dz/dt=-x-z^3

Using the Lyapunov function as follows

V(x,z)=(x^2+z^2)

1. By applying LaSalle's invariance principle what can be said about the stability of the system?
2. What kind of mechanical system we can think of here?
3. If the output is y=z, construct an observer for the system.

[Steven Lord]

This sounds like a homework assignment. If that's correct, show us the code you've written so far to try to solve the problem and ask a specific question about where exactly you're having difficulty and you may receive some guidance.