Question

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

I got this question in an online quiz.

I'm obligated to ask this question of The Infinite Time Regulator Problem topic in section Optimal Control Systems of Control Systems

Answer 1

Right answer is (b) The asymptotic stability is not guaranteed

The best I can explain: If the plant is controllable and bounded and in infinite state regulators the asymptotic stability is not guaranteed even if the Q is positive and semi-definite.