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

Using matlab to solve Lyapunov function

Tran Paul

2018 11 18

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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)

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

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Steven Lord 2018-11-18

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.

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