Question

Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?

• A. All the poles of the system must lie on the left side of the $j\omega$ axis.
• B. Zeros of the system can lie anywhere in the $s$-plane.
• C. All the poles must lie within $|s|=1$.
• D. All the roots of the characteristic equation must be located on the left side of the $j\omega$ axis.

Hint:

Do not confuse continuous-time stability conditions with discrete-time stability conditions.

Answer 1

The Correct Option is C

Step 1: Stability condition for continuous-time LTI systems.
For a continuous-time causal and stable LTI system, all poles must lie strictly in the left half of the $s$-plane.
Step 2: Analyze each option.
Option (A): Correct — poles must lie on the left of the imaginary axis.
Option (B): Correct — zeros do not affect stability and can be anywhere.
Option (C): Incorrect — the condition $|s|<1$ applies to discrete-time systems, not continuous-time systems.
Option (D): Correct — roots of the characteristic equation are poles and must lie in the left half-plane.
Step 3: Final conclusion.
Hence, option (C) is NOT true for a continuous-time causal and stable LTI system.