Transformation: State Space ↔ Pole-Zero

Given a state space representation it is possible to derive a pole-zero model directly, but it is more convenient to go first derive the transfer function, and then go from the transfer function to the pole-zero model model.

Example: State Space → Pole-Zero

Find a pole-zero model for the system described by the state space representation:


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


Step 2: Find a pole-zero representation using the methods described here (TF ↔ PZ).  The pole-zero representation consists of:

Example: Pole-Zero → State Space

Repeat the previous example, but reverse the order (i.e., do step 2 (PZ → 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