This set of Control Systems Multiple Choice Questions & Answers (MCQs) focuses on “Liapunov’s Stability Criterion – I”.

1. A system is said to be locally stable if:

a) The region S (e) is small

b) There exist a real number >0 such that || x (t0) || <=r

c) Every initial state x (t0) results in x (t) tends to zero as t tends to infinity

d) They are unstable

2. The system is asymptotically stable at the origin if :

a) It is stable

b) There exist a real number >0 such that || x (t0) || <=r

c) Every initial state x (t0) results in x (t) tends to zero as t tends to infinity

d) It is unstable

3. If the system is asymptotically stable irrespective that how close or far it is from the origin then the system is:

a) Asymptotically stable

b) Asymptotically stable in the large

c) Stable

d) Unstable

4. The system is asymptotically stable in the large at the origin if :

a) It is stable

b) There exist a real number >0 such that || x (t0) || <=r

c) Every initial state x (t0) results in x (t) tends to zero as t tends to infinity

d) Both a and c

5. The direct method of Liapunov is :

a) Concept of energy

b) Relation of stored energy

c) Using the equation of the autonomous systems

d) All of the mentioned

6. The visual analogy of the Liapunov energy description is:

a) Ellipse

b) Circle

c) Square

d) Rectangle

7. The stability of non-linear systems:

a) Disturbed steady state coming back to its equilibrium state

b) Non-linear systems to be in closed trajectory

c) In limit cycles that is oscillations of the systems

d) All of the mentioned

8. The results for the energy :

a) Energy of the system is non-negative

b) Energy of the system decreases as t increases

c) Energy is non-negative and decreases as t increases

d) Energy is negative

9. The idea that the non-negative scalar functions of a system state can also answer the question of stability was given in Liapunov function:

a) True

b) False

10. The method of investigating the stability using Liapunov function as the ________________

a) Direct method

b) Indirect method

c) Not determined

d) Always unstable