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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 methodThis question was addressed to me in a national level competition.The origin of the question is The Direct Method andConstructing of Liapunov for the Linear and Non-Linear System in division Liapunov’s Stability Analysis of Control Systems

Answer»

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.



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