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A system is described by the state equation X· = AX + BU. The output is given by Y = CX, where
A = 
-4 -1 
, B = 1 , C = [1 0] 3 -1 1
The transfer function G(s) of the system is—
-
- s/s2 + 5s + 7
- 1/s2 + 5s + 7
- s/s2 + 3s + 2
- 1/s2 + 3s + 2
- s/s2 + 5s + 7
Correct Option: A
The transfer function G(s) of the system is given by relation
G(s) = C(SI – A)–1 B + D
where given,
| A = | = | | | ||
| -1 | 3 |
| B = | | | |
| 1 |
C = [1 0]
D = 0
and I is the identity matrix of 2 × 2. Now
| (sI – A) = | | | - | | | ||||
| 0 | s | 3 | -1 |
| (sI – A) = | | | ||
| - 3 | s + 1 |
| | |||
| (sl -A)-1 = | +3 | s + 1 | ||
| (s + 4) (s + 1) + 3 | ||||
| | |||
| + 3 | s + 4 | |||
| s2 + 5s + 7 | ||||
| | ||||
| G(s) = [1 0] | + 3 | s + 4 | | | |
| s2 + 5s + 7 | |||||
| G(s) = | | | = | |||
| s2+ 5s + 7 | 1 | s2+ 5s + 7 |
| G(s) = | |
| s2+ 5s + 7 |
Hence alternative (A) is the correct choice.
