Problem 2 Proving and Designing for Stability (15 pts.) Consider a closed-loop system with unity gain...

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Problem 2 Proving and Designing for Stability (15 pts.) Consider a closed-loop system with unity gain feedback. a. For the following cases, use Routh's stability criterion to determine whether the closed-loop system is stable, how many roots of the closed-loop system have negative real parts, and how many roots do not have negative real parts. After solving the problem, you can check your answers using the roots function in MATLAB. Note: Be sure to find the characteristic equation for the closed-loop system first. (10 pts.) i. D(s)G(s) = ii. D(s)G(s) = 2(s+4) s (s+1) (s+5)(s-5) s (s+4) (Hint: This requires special handling.) Problem 2 Proving and Designing for Stability (15 pts.) Consider a closed-loop system with unity gain feedback. a. For the following cases, use Routh's stability criterion to determine whether the closed-loop system is stable, how many roots of the closed-loop system have negative real parts, and how many roots do not have negative real parts. After solving the problem, you can check your answers using the roots function in MATLAB. Note: Be sure to find the characteristic equation for the closed-loop system first. (10 pts.) i. D(s)G(s) = ii. D(s)G(s) = 2(s+4) s (s+1) (s+5)(s-5) s (s+4) (Hint: This requires special handling.)