3. Consider the state equation d x1 dt x2 with initial conditions 0 4 = -4 0 đ] ( x1 (7) x2 x1(0) ) ΧΟ x2(0) Determine the response x1(t) and x2(t) of the system by using the following two methods. (a) Determine the eigenvalues and eigenvectors of the state matrix. Derive x1(t) and x2(t) via eigenvector expansion. (b) Determine the state transition matrix using the series expansion eAt = I + At+ A2+2 A3+3 + +... 2! 3! to the fifth power. Derive x1(t) and x2(t) in terms of infinite series. (9)
3. Consider the state equation d x1 dt x2 with initial conditions 0 4 = -4 0 đ] ( x1 (7) x2 x1(0) ) ΧΟ x2(0) Determine the response x1(t) and x2(t) of the system by using the following two methods. (a) Determine the eigenvalues and eigenvectors of the state matrix. Derive x1(t) and x2(t) via eigenvector expansion. (b) Determine the state transition matrix using the series expansion eAt = I + At+ A2+2 A3+3 + +... 2! 3! to the fifth power. Derive x1(t) and x2(t) in terms of infinite series. (9)
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
![3. Consider the state equation
d
x1
dt
x2
with initial conditions
0
4
=
-4
0
đ] (
x1
(7)
x2
x1(0)
)
ΧΟ
x2(0)
Determine the response x1(t) and x2(t) of the system by using the following two methods.
(a) Determine the eigenvalues and eigenvectors of the state matrix. Derive x1(t) and x2(t)
via eigenvector expansion.
(b) Determine the state transition matrix using the series expansion
eAt = I + At+
A2+2 A3+3
+
+...
2!
3!
to the fifth power. Derive x1(t) and x2(t) in terms of infinite series.
(9)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1720cd77-2294-45a6-8b70-43447dc02920%2F0f043d5e-9fae-4468-84f8-1f0fc42b9e14%2Fjtw509h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Consider the state equation
d
x1
dt
x2
with initial conditions
0
4
=
-4
0
đ] (
x1
(7)
x2
x1(0)
)
ΧΟ
x2(0)
Determine the response x1(t) and x2(t) of the system by using the following two methods.
(a) Determine the eigenvalues and eigenvectors of the state matrix. Derive x1(t) and x2(t)
via eigenvector expansion.
(b) Determine the state transition matrix using the series expansion
eAt = I + At+
A2+2 A3+3
+
+...
2!
3!
to the fifth power. Derive x1(t) and x2(t) in terms of infinite series.
(9)
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