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# Solving State Space Representation

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

x'1 1 1 0 x1 2

x'2 = 0 -1 1 x2 + -1 u

x'3 13 -1 -2 x3 -2

y = [1 1 0]x

a) Check the stability of the system
b) Design a feedback controller to move (only) the unstable pole to s= -3.
c) Check that the closed loop system will have the required eigenvalues.

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Wow! it is quite a tedious task. Please see the attached file.

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

x'1 1 1 0 x1 2

x'2 ...

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## State Space Representation: Control and Design

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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