What This Question Is Really Testing

Two different ideas are being tested: closed-loop stability and robustness to parameter variation . Negative feedback can improve both in many practical designs, but it guarantees neither simply because the feedback sign is negative.

Concept Foundation

For a standard negative-feedback loop:

T(s) = G(s)/[1 + G(s)H(s)]

Characteristic equation: 1 + G(s)H(s) = 0

The roots of the characteristic equation are the closed-loop poles. Their locations decide stability.

Step 1 — Evaluate Statement 1

Statement 1 is false. Negative feedback does not automatically force all closed-loop poles into the left half-plane. If the loop gain and phase cause the characteristic equation to have unstable roots, the closed-loop system is unstable even though the feedback connection is negative.

Step 2 — Evaluate Statement 2

Statement 2 is true. One important benefit of negative feedback is reduced sensitivity to changes in forward-path parameters.

S = 1/[1 + G(s)H(s)]

When the loop gain is appropriately large and the loop remains stable, the sensitivity magnitude can become much smaller than one.

Step 3 — Select the Statement Combination

Statement 1 is false and Statement 2 is true. Hence the correct option is C .

Why This Method Works

The denominator 1 + G(s)H(s) simultaneously explains both ideas: its roots govern stability, while the same loop-gain term appears in the sensitivity reduction factor.

Independent Verification / Cross-Check

The logic is internally consistent: a system can be robust to moderate parameter changes yet still require an independent stability check from poles, Routh, Nyquist or Bode margins.

Concept Extension

• Negative feedback commonly reduces sensitivity and steady-state error.
• It may increase bandwidth.
• Improper loop phase or excessive gain can still create instability.

Exam Strategy

In statement questions, watch absolute words such as always . Separate “feedback benefit” from “guaranteed stability,” then judge each statement independently.

Quick Trick

“Always stable” is too strong; “may improve robustness” is valid.

Why Other Options Are Wrong

A and B incorrectly accept Statement 1. D incorrectly rejects the valid robustness statement. Only C matches “Statement 1 false, Statement 2 true.”

Common Mistake

Equating “negative feedback usually improves stability” with “negative feedback always guarantees stability.”

What This Question Is Really Testing

Two different ideas are being tested: closed-loop stability and robustness to parameter variation . Negative feedback can improve both in many practical designs, but it guarantees neither simply because the feedback sign is negative.

Concept Foundation

For a standard negative-feedback loop:

T(s) = G(s)/[1 + G(s)H(s)]

Characteristic equation: 1 + G(s)H(s) = 0

The roots of the characteristic equation are the closed-loop poles. Their locations decide stability.

Step 1 — Evaluate Statement 1

Statement 1 is false. Negative feedback does not automatically force all closed-loop poles into the left half-plane. If the loop gain and phase cause the characteristic equation to have unstable roots, the closed-loop system is unstable even though the feedback connection is negative.

Step 2 — Evaluate Statement 2

Statement 2 is true. One important benefit of negative feedback is reduced sensitivity to changes in forward-path parameters.

S = 1/[1 + G(s)H(s)]

When the loop gain is appropriately large and the loop remains stable, the sensitivity magnitude can become much smaller than one.

Step 3 — Select the Statement Combination

Statement 1 is false and Statement 2 is true. Hence the correct option is C .

Why This Method Works

The denominator 1 + G(s)H(s) simultaneously explains both ideas: its roots govern stability, while the same loop-gain term appears in the sensitivity reduction factor.

Independent Verification / Cross-Check

The logic is internally consistent: a system can be robust to moderate parameter changes yet still require an independent stability check from poles, Routh, Nyquist or Bode margins.

Concept Extension

• Negative feedback commonly reduces sensitivity and steady-state error.
• It may increase bandwidth.
• Improper loop phase or excessive gain can still create instability.

Exam Strategy

In statement questions, watch absolute words such as always . Separate “feedback benefit” from “guaranteed stability,” then judge each statement independently.

Quick Trick

“Always stable” is too strong; “may improve robustness” is valid.

Why Other Options Are Wrong

A and B incorrectly accept Statement 1. D incorrectly rejects the valid robustness statement. Only C matches “Statement 1 false, Statement 2 true.”

Common Mistake

Equating “negative feedback usually improves stability” with “negative feedback always guarantees stability.”

What This Question Is Really Testing

Two different ideas are being tested: closed-loop stability and robustness to parameter variation . Negative feedback can improve both in many practical designs, but it guarantees neither simply because the feedback sign is negative.

Concept Foundation

For a standard negative-feedback loop:

T(s) = G(s)/[1 + G(s)H(s)]

Characteristic equation: 1 + G(s)H(s) = 0

The roots of the characteristic equation are the closed-loop poles. Their locations decide stability.

Step 1 — Evaluate Statement 1

Statement 1 is false. Negative feedback does not automatically force all closed-loop poles into the left half-plane. If the loop gain and phase cause the characteristic equation to have unstable roots, the closed-loop system is unstable even though the feedback connection is negative.

Step 2 — Evaluate Statement 2

Statement 2 is true. One important benefit of negative feedback is reduced sensitivity to changes in forward-path parameters.

S = 1/[1 + G(s)H(s)]

When the loop gain is appropriately large and the loop remains stable, the sensitivity magnitude can become much smaller than one.

Step 3 — Select the Statement Combination

Statement 1 is false and Statement 2 is true. Hence the correct option is C .

Why This Method Works

The denominator 1 + G(s)H(s) simultaneously explains both ideas: its roots govern stability, while the same loop-gain term appears in the sensitivity reduction factor.

Independent Verification / Cross-Check

The logic is internally consistent: a system can be robust to moderate parameter changes yet still require an independent stability check from poles, Routh, Nyquist or Bode margins.

Concept Extension

• Negative feedback commonly reduces sensitivity and steady-state error.
• It may increase bandwidth.
• Improper loop phase or excessive gain can still create instability.

Exam Strategy

In statement questions, watch absolute words such as always . Separate “feedback benefit” from “guaranteed stability,” then judge each statement independently.

Quick Trick

“Always stable” is too strong; “may improve robustness” is valid.

Why Other Options Are Wrong

A and B incorrectly accept Statement 1. D incorrectly rejects the valid robustness statement. Only C matches “Statement 1 false, Statement 2 true.”

Common Mistake

Equating “negative feedback usually improves stability” with “negative feedback always guarantees stability.”