Question

Consider the following statements:
A system is said to be stable if its output is bounded for any input.
A system is stable if all the roots of the characteristic equation lie in the right half of the s-plane.
A system is stable if all the roots of the characteristic equation have negative real parts.
A second order system is always stable for finite positive values of open loop gain. Which of the above statements are correct?

• A. B, C and D
• B. A only
• C. B and C
• D. C and D

Hint:

A system is stable if the roots of the characteristic equation lie in the left half of the s-plane or if they have negative real parts.

Answer 1

The Correct Option is C

- Statement A is incorrect because a system is stable if the output is bounded for all bounded inputs, not for any input.
- Statement B is correct: A system is stable if all the roots of the characteristic equation lie in the left half of the s-plane.
- Statement C is correct: A system is stable if all the roots of the characteristic equation have negative real parts.
- Statement D is incorrect: A second order system may not be stable for finite positive values of open-loop gain; it depends on the damping ratio and natural frequency.
Thus, the correct answer is B and C.