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 jw 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 jw axis.

Answer 1

i think the correct option is C

Answer 2

Answer:

(C) "All the poles must lie within s = 1." is NOT TRUE for continuous time casual and stable LTI system.

Step-by-step explanation:

Conditions for poles and zeros of Transfer function is:

• Poles and zeros are either real or occur in conjugate pairs.
• Poles and zeros on the jw- axis will always be simple.
• The real part of all poles and zeros must either be negative or zero. Thus, all poles and zeros must lie on the left half of the s-plane or on the imaginary axis.

• From the above conditions for Poles and Zeros of transfer function for a linear time invariant system, it is clearly evident that OPTION A, OPTION B, OPTION D holds good
• Hence, OPTION C is NOT TRUE for continuous time casual and stable linear time invariant system.