Homework 2
Due Sep 28, 2016 in Class
Please write down who you collaborated with,
your student ID number, and how long you
spent.
Problem 1: 20 points
Consider the nonlinear system x = x2 u, x(0) = 1, y = x + x3 .
(a) Please find the solution of this syst

Solution for HW2
1
Problem 1
2
(a) From dx
= x2 t, we obtain x12 dx = tdt. Thus x1 = t2 + c. Hence
dt
x(t) = t21 . From the initial condition x(0) = 1, we get c = 1. Thus
+c
2
,
t2 +2
2
x(t) =
and y(t) =
2
t2 +2
+ ( t22+2 )3 .
(b) Let us denote the soluti

Solution for HW3
1
Problem 1
(a) From the ODE, we obtain the transfer function from u to y as
Y (s)
s+1
s+1
= 2
=
U (s)
s + 7s + 12
(s + 3)(s + 4)
H(s) =
However, by partial fraction expansion, we have
a
b
s+1
=
+
.
(s + 3)(s + 4)
s+3 s+4
We then find a a