FUND OF ENG THERMODYN(LLF)+WILEYPLUS
9th Edition
ISBN: 9781119391777
Author: MORAN
Publisher: WILEY
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In class, two approaches—Theorems 1 and 2 below—are discussed to prove asymptotic stability of asystem when ̇V = 0.
Show the asymptotic stability of the system given in Eq. (1) by applying Theorem 1.
Show the asymptotic stability of the system given in Eq. (1) by applying Theorem 2.
Homework#5
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.
Using linear stability analysis, show that the system is asymptotically stable.
Hint: stability of a linear system z_dot = Az is characterized by the eigenvalues of A.
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