Uniqueness of State-Space Model

Correct Answer

C — Statement 2 is correct, but statement 1 is incorrect.

Statement-wise Analysis

Statement 1: False

Statement 2: True

Concept and Reasoning

A given input-output system can have many state-space realizations related by nonsingular similarity transformations, so a state model is not unique. A transfer function can, however, be realized in state-space form. Thus statement 1 is false and statement 2 is true.

Calculation / Key Relation

x=Tz ⇒ A′=T⁻¹AT, B′=T⁻¹B, C′=CT

Exam Takeaway

Transfer function can have many equivalent state realizations.

Common Mistake

Do not confuse an equivalent realization with a unique realization.