Problem 3 [28 points, 4 points each] Consider the continuous-time linear time-invariant system with transfer-function: Answer the following questions: a. What is the differential equation associated with the above transfer-function? b.

Calculate the poles and zeros of G(s). c. Is G(s) asymptotically stable? d. Use the bilinear transformation (aka Tustin transformation) S = 2 z 1 Tsz + 1 to calculate the corresponding discretized transfer-function Ga(z). e. Calculate the poles and zeros of Ga(z). f. Is Ga(z) asymptotically stable? (A discrete-time system is asympotically stable if the poles satisfy |pi|< 1.) g. Use a computer program or calculator to sketch the magnitude and the phase of the frequency response G(jw). Now sketch the magnitude and phase of Gd(es) as a function of w when Ts = {0.01, 0.1, 1}s. Compare all the obtained responses. What is the role of Ts?