Consider the system i = Ax + Bu, where 0 -6 0 - 1 -1 3 -1 1 -2 1 -1 1 -2 1 6 -2 1 -1 A = 1 B = -1 -1 2 1 1 -2 0 -2 -1 (a) Show that -1 is an uncontrollable eigenvalue.

Advanced Engineering Mathematics
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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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4.5. Consider the system i = Ax + Bu, where
%3D
0 -6
0 - 1
-1
3
1
-2
1
-1
-1
-2
1
6 -2
1
0 -1
A =
1
B =
-1
2
-1
2
1
1
2
0 0
(a) Show that -1 is an uncontrollable eigenvalue.
-2
0 -2
-1
Transcribed Image Text:4.5. Consider the system i = Ax + Bu, where %3D 0 -6 0 - 1 -1 3 1 -2 1 -1 -1 -2 1 6 -2 1 0 -1 A = 1 B = -1 2 -1 2 1 1 2 0 0 (a) Show that -1 is an uncontrollable eigenvalue. -2 0 -2 -1
Expert Solution
Uncontrollable Eigenvalue

For a system x.=Ax+Bu, an eigen value λ of matrix An×n is said to uncontrollable if rankA-λI Bn.

Given system is x.=Ax+Bu, where:

                            A=-100-63-11-210-1-11106-21100000-12-1021-200-20-1,   B=01-1-20-1001200

and given eigen value is λ=-1.

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