Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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If you have a spring mass damper system, given by m*x_double_dot + c*x_dot + kx = 0 where m, c, k (all positive scalars) are the mass, damper coefficient, and spring coefficient, respectively. x ∈ R represents the displacement of the mass.
Let us then discuss the stability of the system by using Lyapunov stability theorem. Consider the system energy as a candidate Lyapunov function shown in the image.
Discuss the positive definiteness of V (x, x_dot).
Derive the Lyapunov rate of this system (i.e., V_dot ), and discuss the stability property of the
system based on the information we gain from ̇V_dot .
Transcribed Image Text:V (x, x) = m² + 1/kx²
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