AE 350 Problem Set #1
Issued: Sept. 15, 2025
Due: Sept. 25, 2025 (11:59pm)
1. For each of the following transfer function, write the corresponding differential equation:
Y (s)
12
= 2
U (s)
s + 8s + 12
2s + 3
Y (s)
=
(b)
U (s)
(s + 1)(s + 2)(s − 1)
(a)
2. Find the transfer function for the following differential equations:
...
(a) y − 2ÿ + ẏ − 2y = u̇ + 2u
(b) ÿ + 4ẏ + 3y = 3u
3. Find the transfer function G(s) = Y (s)/U (s) for each of the following systems in state-space
representation:
 


0
0
1 −1



y = 1 0 −1 x
(a) ẋ = −1 −3 0 x + 2 u,
0
1
0 −1
0 1
2
(b) ẋ =
x+
u,
y = 1 −1 x
−1 0
1
4. Find a state-space representation of the following transfer function:
10
(s − 4s + 10)
s+1
(b) G(s) =
(s − 1)(s + 2)(s2 + 2s + 4)
(a) G(s) =
1