State Space Variable Dependencies, Working with interdependent state vars

[cstobart]

Hi Everyone,

I am working on a state space model for an electromechanical system. Part of the issue is the internal state vector ends up having interdependencies.
Take the following state vector as an example:

X = x1
x2
x3
(x1/x2)^2
1 - x1

This would be the vector in the dX = AX + BU

Ultimately my problem is how can a find an equilibrium point with a change of coordinates if the last part of the above vector is dependent on the first. The change of coordinates needs to happen to allow for Lyapunov stability analysis around the equilibrium point of the system. Is there a way to work around this issue? Is it an issue at all?

Any input would be greatly appreciated.
Thank You.

[tashirosgt]

Aren't the state variables supposed to be the smallest number of variables needed to represent the state of the system? If so, you shouldn't have a state variable that is a function of other state variables.