Consider the following system whose state space representation is as follows:
x'1 -1 1 α x1 0
x'2 = 0 -2 1 x2 + 0 u
x'3 0 0 -3 x3 1
y = [1 0 0]x
a) Draw the block diagram representation of the system.
b) Find the transfer function of the system.
c) Are there any values of α for which the system would be unstable?
d) Using the transfer function, determine for which value(s) of α the system is unstable.
e) Is the system controllable when α tends to infinity? Explain your answer.
f) Using the controllability matrix, check the answers found in (d) and (e).
Solution includes block diagram drawing and explanations using transfer function.