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

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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

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