# The Infinite-Time Regulator Problem MCQ’s

This set of Control Systems Multiple Choice Questions & Answers (MCQs) focuses on “The Infinite-Time Regulator Problem”.

1. When time and the state variables tend to infinity then the system becomes:
a) Unstable
b) Stable
c) Marginally stable
d) Conditionally stable

2. In finite time regulator:
a) There is no restriction on the controllability of the plant
b) Performance index is infinite
c) Instability imposes problem in finite-interval control
d) No restriction on controllability and performance index

3. In infinite time regulator for the final time is:
a) t1
b) t0
c) Infinite
d) Zero

4. Performance index can become infinite if:
a) One or more state are uncontrollable
b) The uncontrollable states are uncontrollable
c) The unstable states are reflected in system performance index
d) All of the mentioned

5. The differential term in the riccati equation in infinite regulator is:
a) Finite
b) Positive
c) Infinite
d) Zero

6. If Q is positive semi- definite:
a) The optimal closed loop system is asymptotically stable
b) The asymptotic stability is not guaranteed
c) The system is stable
d) The system is unstable

7. In Infinite regulator the optimal control cannot be differentiated from other controls.
a) True
b) False

8. The solution of the modified riccati equation may be:
a) Independent
b) Dependent
c) Unique
d) Non-unique

9. Tracking problem can be in:
a) Infinite state regulators
b) Finite state regulator
c) Sub-optimal state regulators
d) Non-linear regulators

10. The regulators that convert the non-linear stability into linear stability:
a) Linear
b) Sub-optimal
c) Finite
d) Infinite