Consider the system given by

with

so that

Now consider the definition of a new set of state variables:

In terms of the original state variables

or

We now restate the original state representation and plug this definition of
**q**, and solve

This gives us our new state space representation

with

Details of the solution (with MatLab) are here (html, .m).

© Copyright 2005 to 2015 Erik Cheever This page may be freely used for educational purposes.

Erik Cheever Department of Engineering Swarthmore College