A system is given by the input-output differential equation.
Where u = input, y = output.
a. Using Routh-Hurwitz criterion (and without solving the characteristic equation), determine how many poles of the system are on the LHP. Is the system stable?
b. For a unit step input, determine the steady-state value of the response, by using the differential equation and explaining your rationale. Next, verify your answer using FVT. Suppose that all the poles of the given system are moved to the right by 1 (and the system zeros are not changed).
c. Using Routh-Hurwitz criterion (and without actually solving the characteristic equation) determine the stability of the new system (with moved poles).