Consider the continuous-time system described by the transfer function:
s + 1 / H(s) = s^2 + 100
a) Write the differential equation describing the system. Use v to denote the input signal and y to denote the output signal.
b) The impulse response h(t) of the system is of the form:
h(t) = acos(bt) + csin(dt) for all t ∈ R+
where a, b, c, and d are real numbers. Determine a, b, c, and d, showing all steps.
c) Is this a causal system? Explain your answer.
d) Determine a state space representation (A, B, C, D) in controller canonical form for the system.
e) Determine a state space representation (A, B, C, D) for the system such that A is a diagonal matrix.
f) Compute the transfer function that corresponds to your answer to part e). Use this computation to check that your answer to part e) is correct.
g) Yuting claims that there exists a frequency ω such that the system's response to v(t) = v(t)sin(ωt) is unbounded. Robin disagrees. Whose side are you on and why? Explain in detail.
