4. A čóntinuóus time dynamic system is described by [0] x'(t) =|-2.5 -7 4 x+ 0 u(t), t2 0 O -5 -1 2 [1] y(t) = [1 2 0]x(t) a. Use the Cayley-Hamilton remainder technique, i.e. e^t = a6(t)I + a,(t)A + az(t)A² to obtain the state transition matrix ¤(t). b. Obtain the transfer function G(s).

4. A čóntinuóus time dynamic system is described by [0] x'(t) =|-2.5 -7 4 x+ 0 u(t), t2 0 O -5 -1 2 [1] y(t) = [1 2 0]x(t) a. Use the Cayley-Hamilton remainder technique, i.e. e^t = a6(t)I + a,(t)A + az(t)A² to obtain the state transition matrix ¤(t). b. Obtain the transfer function G(s).

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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Differential Equations

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Question

4. A continuous time dynamic system is described by
[0]
x'(t) =|-2.5 -7 4 x+0 u(t), t20
O -5
-1
2
y(t) = [1 2 0]x(t)
a. Use the Cayley-Hamilton remainder technique, i.e. et = a6(t)I + a, (t)A + a,(t)A?
to obtain the state transition matrix 0(t).
b. Obtain the transfer function G(s).

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