Question

Consider Example 20 mi $x_1 = \begin{bmatrix} 0 \\ 1 \end{bmatrix} x_1 + \begin{bmatrix} 1 \\ 0 \end{bmatrix} u$ y(t) = \begin{bmatrix} 1 & -2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} (a) Solve for x(t) and y(t). (b) Evaluate H(s) and h(t). t \ge 0 u(t) = \begin{cases} 1 & t \ge 0 \\ 0 & t < 0 \end{cases} time – Two approaches to solve the state equation • Time domain • s-domain

          Consider
Example 20 mi
$x_1 = \begin{bmatrix} 0 \\ 1 \end{bmatrix} x_1 + \begin{bmatrix} 1 \\ 0 \end{bmatrix} u$
y(t) = \begin{bmatrix} 1 & -2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}
(a) Solve for x(t) and y(t).
(b) Evaluate H(s) and h(t).
t \ge 0
u(t) = \begin{cases} 1 & t \ge 0 \\ 0 & t < 0 \end{cases}
time
– Two approaches to solve the state equation
• Time domain
• s-domain

Consider
Example 20 mi
x1 =
< b m a t r i x >
x1 +
< b m a t r i x >
u
y(t) =
< b m a t r i x >

< b m a t r i x >

(a) Solve for x(t) and y(t).
(b) Evaluate H(s) and h(t).
t ≥0
u(t) = 1 t ≥0
0 t < 0
time
– Two approaches to solve the state equation
• Time domain
• s-domain

Added by Glenda W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Carson Merrill

01/14/2022

Step 1

Step 1: Write the state-space representation of the system: Given: ẋ₁ = ẋ₁ ẋ₂ = [0, 1, -3]x₁ - 2x₁ + 0u y = [1, -2]x₁ Show more…

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Thanks for your feedback!

[[x_(1)^(˙)]] x_(2)^(˙)=[[0,1,-3]] -2[[x_(1)]] x_(2)+[[0]] 1u y(t)=[[1,-2]][[x_(1)]] x_(2) [[x_(1)(0)]] x_(2)(0)=[[-1]] 1 u(t)={(1,t>=0):} 0,t<0 市 ∩ n (a) Solve for x(t) and y(t). (b) Evaluate H(s) and h(t). Two approaches to solve the state equation: 1. Time domain 2. s-domain s-domain Time domain (b) Evaluate H(s) and h(t) (a) Solve for x(t) and y(t) Consider -- Two approaches to solve the state equation [1-[21+1 Example time 3