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Root Locus and Routh-Hurwitrz

Please help solving this problem without matlab:
a. Use Routh-Hurwitz to find vales of K so that L = k (s+1) / (s^2 +4) (s+10) has poles to the left of s= -2
b. Make a sketch of the root-locus of the above L(s) to explain the results above. You need to calculate the asymptotes (as s and k go to infinity) and angles of departure. There are no real axis break points on the positive gain root locus.

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Solution Summary

This solution uses relative analysis and the Routh-Hurwitz Stability Test to determine the poles of the equation and also sketches the root-locus. All steps and formulas are shown.