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System state space representation

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 Summary

Solution includes block diagram drawing and explanations using transfer function.