EEE 241
EXERCISES FOR CHAPTER 6
Instructor: Prof. M. Heller
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Print Name __________________________________________last 4 digits of SID______________
Problem 6.1 (Page 180)
Determine if the system is Controllable and Observable using the Controllability Matrix,
Observability Matrix, Wc(t) found in (6.2), and, Wo(t) found in (6.28). Use MATLAB. You do not
need to write to solutions for Wc(t) and Wo(t) . Justify your answer;
Controllable?______ Why?____________________________________________________________
Observable?______ Why?_____________________________________________________________
Problem 6.10 (Page 181): For Problem 6.10 in the textbook, y should be: y= [0 1 0 1 1].
Select 1  3 and  2  5 .
Reduce the system given in Problem 6.10 to a Controllable Subset-State Equation:
EEE 241
EXERCISES FOR CHAPTER 6
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Reduce the system given in Problem 6.10 to an Observable Subset-State Equation:
Reduce the system given in Problem 6.10 to a Controllable and Observable Subset-State Equation:
EEE 241
EXERCISES FOR CHAPTER 6
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Problem 6.19 (Page 182)
a) Using the controllable system in Problem 4.2 (Page 117), find the u(t) that will drive the
continuous system state of Problem 4.2 from X= [0;0] to X= [1;2] in 4 seconds using minimum
energy.
EEE 241
EXERCISES FOR CHAPTER 6
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b) a) Using the controllable system in Problem 4.2 (Page 117), determine the sampling periods T for
which the discretized system is uncontrollable. Also, find the discretized system using c2d.m and
check to see if it is controllable for T = pi.
T for which the sample data system is uncontrollable= ______________________________________
Rank of Discretized System for T= pi : Rank =___________
T selected for your discrete system is ____________. State Realization of Discretized System is:
EEE 241
EXERCISES FOR CHAPTER 6
Problem 6.20 (Page 182)
Determine if the LTV system is Controllable and/or Observable.
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Controllable?______ Why?____________________________________________________________
Observable?______ Why?____________________________________________________________