5. For the control system represented by the following state space model -+- y = [10¹] 2e-t-e-2t 1 (t) = -2¹ +2²2 e-t-e-t +22), then the system response (x,(0.13(6) dec to the initial condition x(0)=[] is given as ₁ (t) a. [x₁(0)1 [x₂ (1)) x₂ (1) -(2a + b)e+(a+b)e-2] (2a + b)et(2a + 2b)e-2 (a+2b)e-(a+b)" -(a+2b)e+ (2a +26) = Lx₂ (1) (2a + b)e-(a + b)e-21 + d. None of the answers

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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5. For the control system represented by the following state space model
-12-9-
y=[10][x]
2e-t-e-2t
et-e-t
If (t) = -2e²+ + 20-21-612) then the system response (x,(0), 4(1)) dise
to the initial condition x(0)=[] is given as
[x₂(t)]
a.
=
[x₁(0)1
[x₂ (1))
-
[-(2a + b)et + (a + b)e-2)
+
(a +2b)e-(a+bje"
-(a+2b)e+ (2a + 2bje"
[x₂ (t).
(2a + b)et(a+b)e-2
+
C.
d. None of the answers
Transcribed Image Text:5. For the control system represented by the following state space model -12-9- y=[10][x] 2e-t-e-2t et-e-t If (t) = -2e²+ + 20-21-612) then the system response (x,(0), 4(1)) dise to the initial condition x(0)=[] is given as [x₂(t)] a. = [x₁(0)1 [x₂ (1)) - [-(2a + b)et + (a + b)e-2) + (a +2b)e-(a+bje" -(a+2b)e+ (2a + 2bje" [x₂ (t). (2a + b)et(a+b)e-2 + C. d. None of the answers
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