# Constructing of Liapunov for the Linear and Non-Linear System MCQ’s

This set of Control Systems Multiple Choice Questions & Answers (MCQs) focuses on “Constructing of Liapunov for the Linear and Non-Linear System”.

1. Liapunov’s stability analysis is for the :

a) LTI system

b) Time variant system

c) Non-linear system

d) Linear system

2. The system is unstable for:

a) W (x)>0; x not equal to zero

b) W (0) =0

c) W (x) has continuous partial derivative with respect to all components of x

d) All of the mentioned

3. If the Liapunov’s function cannot be found then the system is:

a) Stable

b) Unstable

c) Conditionally stable

d) Marginally stable

4. Liapunov’s stability for non-linear system is same as the Routh Hurwitz criteria for the linear system.

a) True

b) False

5. It is difficult to form Liapunov’s function for:

a) Linear system

b) Non-linear

c) Time variant systems

d) Time –invariant systems

6. The method which provides considerable flexibility in finding the Liapunov’s function is:

a) Krasovskii’s method

b) Variable gradient method

c) Constant method

d) Non-variable gradient method

7. Conditions of ___________ are necessary and sufficient condition for the asymptotic stability of the system.

a) Linear system

b) Krasovskii’s method

c) positive definiteness

d) Variable gradient method

8. If the V is positive definite, for the system to be asymptotically stable, Q should be negative definite.

a) Krasovskii’s method

b) Variable gradient method

c) Constant method

d) Non-variable gradient method

9. Liapunov stability analysis is different from the classical theories approach of stability.

a) True

b) False

10. For non-linear systems the equation for damping factor as in linear system is called__________

a) Krasovskii’s equation

b) Vander Pol’s equation

c) Constant method

d) Non-variable gradient equation