SF2842: Geometric Control Theory, 2014
Answers of Homework 2
March 6, 2014
1. Solution:
a. x1 = 0 x1 = x1 + ax2 = 0 ax2 = 0.
If a = 0, then we have cAk b = 0 for any k Z+ . Thus, the system does not have relative
degree.
If a = 0, then we have x2 = 0 x2 =
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Solution to Exam of SF2842 Geometric Control Theory
December 14 2012 -
Examiner: Xiaoming Hu, phone 790 71 80, mobile 070-796 78 31.
Allowed written material: All course material
Solution to Final Exam of SF2842 Geometric Control
Theory
December 19 2007, 14-19
We reserve the right to make corrections.
1.
Determine if each of the following statements is true or false and motivate (no
motivation no score) your answer briey (for exam
SF2842: Geometric Control Theory
Solution to Homework 1
For reference only
You may discuss the problems in group (maximal two students in a group), but each of
you must write and submit your own report. Write the name of the person you
cooperated with.
1.
SF2842: Geometric Control Theory, 2012
Answers of Homework 2
December 4, 2012
1.
(a) If a = 0, then V = spancfw_e2 .e3 , e4 , and V ImB = ImB = 0.
If a = 0, then the relative degree of the system is 2. Then the system is invertible.
Therefore, the system
SF2842: Geometric Control Theory, 2012
Answers of Homework 2
December 7, 2012
1.
sin (x3 + x4 )
cos (x3 + x4 )
(a) W riggle = [Steer, Drive] =
cos(x4 ) , and
0
cos (x3 + x4 )
sin (x3 + x4 )
[Steer, W riggle] =
sin(x4 ) = g1 ,
0
sin (x3 )
cos (x3
SF2842: Geometric Control Theory, 2014
Answers of Homework 3
March 23, 2014
1. Solution:
2. Solution:
a. True. This can be proved by showing
boundary, namely, xi x0 = r
t xi
x0 2 is negative when xi is already on the
b. False. A counter example can be
x1