8.1 Consider the following transfer function G s s s s s ( ) ( 1) 4 4 2 = + + + (a) Calculate the poles, zeros, relative order and static gain of the system. Is the system BIBO stable? (b) Write down a differential equation that describes the inputoutput behavior of the system in the time domain. (c) Calculate and plot the unit step response. Determine the initial value and the final value of the step response. Can you explain the qualitative shape of the step response? (d) If the input is a ramp with unit slope, what is the asymptotic response of the output? (e) If the input is sinusoidal with unit amplitude and frequency , what is the asymptotic response of the output? (f ) Check your results with MATLAB or Maple.

8.1 Consider the following transfer function G(s)=s2+4s+4s(s+1) (a) Calculate the poles, zeros, relative order and static gain of the system. Is the system BIBO stable? (b) Write down a differential equation that describes the input-output behavior of the system in the time domain. (c) Calculate and plot the unit step response. Determine the initial value and the final value of the step response. Can you explain the qualitative shape of the step response? (d) If the input is a ramp with unit slope, what is the asymptotic response of the output? (e) If the input is sinusoidal with unit amplitude and frequency , what is the asymptotic response of the output