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State Space Representation: Control and Design

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Consider the following system whose state space representation is as follows:

x'1(t) -3 1 x1(t) 1
= + u(t)
x'2(t) -2 1.5 x2(t) 4

x1(t)
y(t) = [ 1 1]
x2(t)

a) Show that the system is not completely controllable.
b) Determine which mode is not controllable.
c) Design a feedback controller such as one of the closed loop poles is located at s= -4.
d) If possible, design an output feedback controller for the system.

See the attached file.

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