Question

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

This question was addressed to me in a national level competition.

The origin of the question is The Direct Method and  Constructing of Liapunov for the Linear and Non-Linear System in division Liapunov’s Stability Analysis of Control Systems

Answer 1

Right choice is (a) Krasovskii’s method

The explanation is: If the V is positive definite, for the system to be asymptotically stable, Q should be negative definite. For Krasovskii’s method and in addition V should tend to infinity and the system is asymptotically stable in-the large.