Dr. Shahruz claims that Theorem 2 in 1 is stronger than Theorem 1 in 2. Since Dr. Shahruz proves his claim by showing an example, not a mathematical derivation, I feel his argument is not convincing. Also it indicates clearly in 2, that the main purpose of the Theorem in 2 is to use damping to eliminate the parametric resonance. So there is no need for considering a time-varying damping.
Gil, M. L., Stability of Finite and Infinite Systems, Kluwer Academic, Dordrecht, 1998.
J. W., and
ASME J. Vibr. Acoust.,
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