Transformation: State Space ↔ Pole-Zero

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:

• a constant term, k=3,
• zeros at s=-1 and s=-2, and
• poles at s=-1+j, s=-1-j and s=-3.

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).