7. (30 Points) Using the Routh-Hurwitz criterion, determine the stability of the closed-loop system that has the following characteristics equations. Determine the number of roots of each equation that are in the right-half s-plane and on j? axis. (a) s³ + 25s² + 10s + 450 = 0 (b) s? + 2s³ + 10s² + 20s + 5 = 0 (c) s? + 2s? + 8s? + 12s? + 20s? + 16s³ + 16s² = 0
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Step 1: Write down the characteristic equation for part (a): \[ s^3 + 25s^2 + 10s + 450 = 0 \] Show moreā¦
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