ME/ECE 851 Fall 2010
Homework # 7
Due Wednesday, November 17, 2010
1. Consider the LQR problem for system
x1 = x2 ,
x2 = x1 + u
and the performance index
[x2 (t) + u2 (t)]dt,
1
J=
>0
0
(a) Find the op
ME/ECE 851 Fall 2010
Homework # 8
Due Wednesday, December 1, 2010
1. Consider the system
x=
01
0 1
0
1
+
u,
1 0 x.
y=
We want to design an output feedback controller such that (i) all closed-loop eige
ME/ECE 851 Fall 2010
Homework # 9
Due Friday, December 10, 2010
1. Consider the continuous-time system
x=
01
0 1
0
1
+
u,
y=
1 0 x.
We want to design a discrete-time output feedback controller such th
ME/ECE 851 Fall 2010
Homework # 6
Due Friday, November 5, 2010
1. Transform the pair
A=
0
3
1
1
01
0
0 3 1
1 4 1
0 1 0
,
B=
0
1
0
0
0
0
1
0
into controller form Ac = P AP 1, Bc = P B . What is the sim
ME/ECE 851 Fall 2010
Homework # 2
Due Friday, September 24, 2010
1. Exercise 3.7
2. Exercise 3.17
3. Exercise 3.19
4. Consider the matrix A given by:
410
A := 0 4 3 .
004
(a) Find the eigenvalues of A
ME/ECE 851 Fall 2010
Homework # 3
Due Wednesday, October 6, 2010
1. Exercise 3.36.
2. Exercise 3.38. Add the following part to the problem.
(c) Investigate asymptotic stability and BIBO stability of t
ME/ECE 851 Fall 2010
Homework # 5
Due Wednesday, October 27, 2010
1. Ex 5.11
2. Ex 6.2
3. Consider the system
x = Ax + Bu, y = Cx + Du.
(a) Show that only controllable modes appear in eAt B , and ther
ME/ECE 851 Fall 2010
Homework # 1
Due Friday, September 10, 2010
1. Exercise 1.10.
2. Find the state model of the circuit of Figure 1.3 when the state variables are taken
as the voltages across the ca