Given the state-space equationsX (t) = 2x(t) + Hu(t) andy(t) = [1 0]X(t)+u(t)(u(t)= 1,t20)If x(0) = [1], what is y(2)?nky

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Answered: Given the state-space equations X(t) =…

Given the state-space equations X(t) = [21]x(t) + [1] u(t) y(t) = [1 0]X(t) +u(t) (u(t)= 1,t≥ 0) If x(0) = [1], what is y(2)? [1]u(t)_and

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.2: Partial Derivatives

Problem 30E

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Question

Given the state-space equations
X (t) = 2x(t) + Hu(t) and
y(t) = [1 0]X(t)+u(t)
(u(t)= 1,t20)
If x(0) = [1], what is y(2)?
nky

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Step 1: Write some Laplace and inverse Laplace transform formulas

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Step 2: Use Laplace transform fo find X(t)

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Step 3: Use inverse Laplace transform

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Step 4: Use inverse Laplace transform formulas

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Step 5: Determine X(t) and y(2)

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Solution

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