Given a system differential equation it is possible to derive a state space model directly, but it is more convenient to go first derive the transfer function, and then go from the transfer function to the state space model.

Find a state space model for the system described by the differential equation:

**Step 1: **Find the transfer function using the methods
described here (1DE ↔ TF)

**Step 2:** Find a state space representation using the
methods described here (TF ↔ SS). In this case we are using a CCF
form).

Repeat the previous example, but reverse the order (i.e., do step 2 (SS → TF) then step 1 (TF → SS)).

© Copyright 2005 to 2019 Erik Cheever This page may be freely used for educational purposes.

Erik Cheever Department of Engineering Swarthmore College