Consider a continuous time, linear, time invariant system such as i(t) Ax(t) + Bu(t) y(t) = Ca(t) + Du(t) = b) Let B = 2e-te²t -e-t + e²t "]. -2e-t +2e²t e-t +2e²t Assume that the state transition matrix is given as a) Determine the system matrix A and its eigenvalues. If we set u(t) = 0 for all t, is the system asymptotically stable? Explain. =[8] and show that the system is controllable.
Consider a continuous time, linear, time invariant system such as i(t) Ax(t) + Bu(t) y(t) = Ca(t) + Du(t) = b) Let B = 2e-te²t -e-t + e²t "]. -2e-t +2e²t e-t +2e²t Assume that the state transition matrix is given as a) Determine the system matrix A and its eigenvalues. If we set u(t) = 0 for all t, is the system asymptotically stable? Explain. =[8] and show that the system is controllable.
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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Question
H3.
![3. Consider a continuous time, linear, time invariant system such as
i(t)
Ar(t) + Bu(t)
y(t) = Cx(t) + Du(t)
-2e-t+2e²t
e-t +2e²t
a) Determine the system matrix A and its eigenvalues. If we set u(t) = 0 for all t, is the system
asymptotically stable? Explain.
=
Assume that the state transition matrix is given as [
b) Let B =
[8]
2e-te²t
+
-e-t + e²t
and show that the system is controllable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb09b6f3-6ca6-46be-9f65-741d9ad22c69%2F06c16f69-f4bd-4ef7-9bcb-8829682039e1%2Fgzwgl0m_processed.png&w=3840&q=75)
Transcribed Image Text:3. Consider a continuous time, linear, time invariant system such as
i(t)
Ar(t) + Bu(t)
y(t) = Cx(t) + Du(t)
-2e-t+2e²t
e-t +2e²t
a) Determine the system matrix A and its eigenvalues. If we set u(t) = 0 for all t, is the system
asymptotically stable? Explain.
=
Assume that the state transition matrix is given as [
b) Let B =
[8]
2e-te²t
+
-e-t + e²t
and show that the system is controllable.
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