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SarkariResultOutBMS · 2024

Previous Year Question

Consider the following statements in the context of state space model of a system.Statement 1:State space model is always unique for a given system.Statement 2:State space model can be derived from the transfer function.Choose the correct options from the following:
  1. Both statement 1 and statement 2 are correct.
  2. Statement 1 is correct, but statement 2 is incorrect.
  3. Statement 2 is correct, but statement 1 is incorrect.
  4. Both statement 1 and statement 2 are incorrect.

Correct answer: C

Explanation

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.

Formula

x=Tz ⇒ A′=T⁻¹AT, B′=T⁻¹B, C′=CT

Step-by-step solution

Uniqueness of State-Space Model explanatory diagram

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.

Common mistake

Do not confuse an equivalent realization with a unique realization.

Exam tip

Transfer function can have many equivalent state realizations.

Quick method

Transfer function can have many equivalent state realizations.