O Choose a similarity transformation matrix T such that T-1 is formed by taking the first two linearly independent columns of C and the last vector as 0012. Then T is given by 1 T = -1 1 -2 1 1 1 0 1 1 T 2 0 0 1 1 1 T = -1 1 1 -2 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve Q3 only
Consider the state matrix A and input matrix B
given by
-1
1
1
A =
1
-2
1
В -
1
1
-1
1
2
2) The rank of the controllability matrix C is
3) Choose a similarity transformation
matrix T such that T-1 is formed by
taking the first two linearly independent
columns of C and the last vector as 0011.
Then T is given by
1
T =
-1
1
1
-2
1
[1
1
17
T =
1
2
1
1
1
T =
-1
1
1
-2
1
Transcribed Image Text:Consider the state matrix A and input matrix B given by -1 1 1 A = 1 -2 1 В - 1 1 -1 1 2 2) The rank of the controllability matrix C is 3) Choose a similarity transformation matrix T such that T-1 is formed by taking the first two linearly independent columns of C and the last vector as 0011. Then T is given by 1 T = -1 1 1 -2 1 [1 1 17 T = 1 2 1 1 1 T = -1 1 1 -2 1
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