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Consider a continuous time, linear, time invariant system such as i(t) Ax(t) + Bu(t) y(t) = Cr(t) + Du(t) = [8] = -2e-t +2e²t Assume that the state transition matrix is given as 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. b) Let B = 2e-te²t -e-te²t 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) = Cr(t) + Du(t) = [8] = -2e-t +2e²t Assume that the state transition matrix is given as 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. b) Let B = 2e-te²t -e-te²t and show that the system is controllable.

Advanced Engineering Mathematics
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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3. Consider a continuous time, linear, time invariant system such as * (t) Ax(t) + Bu(t) y(t) = Cx(t) + Du(t) = 0 2e-te2t -2e-t+2e²t -e-te²t 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. b) Let B = and show that the system is controllable.
Transcribed Image Text:3. Consider a continuous time, linear, time invariant system such as * (t) Ax(t) + Bu(t) y(t) = Cx(t) + Du(t) = 0 2e-te2t -2e-t+2e²t -e-te²t 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. b) Let B = and show that the system is controllable.
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