a. (Routh-Hurwitz Criterion for Stability.) Show that if all of the coefficients of a polynomial are positive, then all of its roots must have negative real parts [10]. b^*. The differential-difference equation d x / d t=-a x(t-1) can be solved using Laplace's transform. Show that the characteristic equation in this case is p=-a e^-p. Consider the roots for p of the function p a e^-p. Show that sin(πt / 2) solves the problem when a=π/ 2. Show that for a<π/ 2 all roots have negative real part. De
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