# Necessary Conditions for Stability and Non-Linear Systems MCQ’s

This set of Control Systems Multiple Choice Questions & Answers (MCQs) focuses on “Necessary Conditions for Stability and Non-Linear Systems”.

1. The disadvantages of the linear system are:
a) The constraints on the linear operation over wide range demands unnecessarily high quality.
b) The restriction to the linear theory may inhibit the designer’s curiosity to deliberately introduce the non-linear components.
c) Practically systems are non-linear
d) All of the mentioned

2. System non-linearities are taken account by:
a) Analytical
b) Graphical and numerical techniques
c) Both a and b
d) None of the mentioned

3. The techniques of linear system can be used in the non-linear system entirely:
a) True
b) False

4. The superposition theorem is :
a) Homogeneity
c) Combination of homogeneity and additivity
d) Applied to non-linear systems

5. The amplitude of the standard test signal does not matter in linear systems:
a) True
b) False

6. The stability of the linear system:
a) Determined by the location of the poles
b) Dependent entirely of whether or the system is driven
c) The stability of the undriven linear system is dependent on the magnitude of the final initial state.
d) Stability cannot be determined by the open loop poles

7. The standard test signal can be applied to give output to:
a) Linear systems
b) Non-linear systems
c) Time variant systems
d) Time invariant systems

8. The non-linear systems:
a) Do not obey superposition theorem
b) May be highly sensitive to the input amplitude
c) Laplace and z transform are not applicable to the non-linear systems
d) All of the mentioned

9. In non-linear system stability is :
a) Dependent on the input
b) Independent on initial state
c) Independent on input
d) Dependent on input and initial state.

10. The necessary condition of stability are:
a) Coefficient of characteristic equation must be real and have the same sign
b) Coefficient of characteristic equation must be non-zero
c) Both of the mentioned
d) Coefficient of characteristic equation must be zero

11. The __________ of the coefficients of characteristic equation is necessary as well as sufficient condition for the stability of system of first and second order.
a) Negativeness
b) Positiveness
c) Positiveness and Negativeness
d) None of the mentioned

12. Non-linear elements may exhibit___________
a) Linear systems
b) Non-linear systems
c) Limit cycles
d) Time invariant systems

13. None of the coefficients can be zero or negative unless one of the following occurs:
a) One or more roots have positive real parts
b) A root at origin
c) Presence of root at the imaginary axis
d) All of the mentioned

14. The Positiveness of the coefficients of characteristic equation is necessary as well as sufficient condition for:
a) First order system
b) Second order system
c) Third order system
d) None of the mentioned

15. Assertion (A): Routh criterion is in terms of array formulation, which is more convenient to handle.
Reason (R): This method is used to investigate the method of stability of higher order systems.
a) Both A and R are true and R is correct explanation of A
b) Both A and R are true and R is not correct explanation of A
c) A is true but R is false
d) A is False but R is true