ECE 717 STATE SPACE SYSTEMS ANALYSIS

• homework 1 (pdf) Due in Ian Dobson's faculty mailbox at 11:59pm Thursday September 11
  
• homework 2 (pdf) Due in Ian Dobson's faculty mailbox at 11:59pm Thursday October 2
  
• homework 3 (pdf) Due in Ian Dobson's faculty mailbox at 11:59pm Thursday October 16
  
• homework 4 (pdf) Due in Ian Dobson's faculty mailbox at 11:59pm Thursday October 30 
• homework 5 (pdf) Due in Ian Dobson's faculty mailbox at midnight Wednesday November 25
• homework 6 (pdf) Due in Ian Dobson's faculty mailbox at 11:59pm Thursday December 4
• homework 7 (pdf) Do not hand in; please make your own solutions and ask Ian if unsure.
  

Matlab files to plot 2D linear vector fields, trajectories and time histories:

Mathematica 6 notebook to plot 2D linear vector fields, trajectories and time histories: linearODE2D.nb

• Instructor: Ian Dobson, 2564 Engineering Hall


• If you have questions or comments for Ian: dobson@engr.wisc.edu
 
• Office hours: 1:30-3:30 pm Wednesday, and after each class 10:50-11:30 am Tuesday and Thursday, or dropping by in the afternoons to ask if I am available, or by appointment in the afternoons. e-mail is effective for short questions. Please use the office hours for questions or feedback about the homework and course material. Most administrative matters can be dealt with by e-mail. I am NEVER available before class because I need to prepare for the class lecture. Please see Ian in person if you are having ANY difficulties with the course (do NOT wait until just before the exams).


• Homework : There will be regular homework which will be an important part of the learning in the course. The homework will be reviewed (to an extent subject to resources being available from the ECE department) but not graded. However the exams will be based on the homework questions. Students are encouraged to work together to solve the homework problems. However, each student must hand in their own work. Students are expected to attempt all homework problems and hand their efforts in.  Homework solutions will not be systematically published, but help is available from the professor. Students are responsible for creating their own portfolio of homework solutions that they can use to study for the exams.  One aspect is that students should work to understand homework well enough that they are confident that their solutions are correct. Success in the course correlates well with consistent and thoughtful effort on the homeworks throughout the course.
  


• Exams : The exams will be closed book written exams intended to assess whether students have mastered the material in the homeworks and the course. There will be a midterm and a final. The midterm will be held at a time most suitable for most students, probably during class time.  The final is at time.  Send email or drop by to Ian in the first two weeks of class if there is ANY chance of religious or other conflicts with these exam times. Exams are designed for the purpose of assessment only and exam papers will not be handed back to students. That is, learning is the focus of the course and the homeworks, but is not a function for the exams.  Students may choose to look at their exam papers for a limited period after the exam by coming to professor office hours. 
  
  
• Class attendance : Students are expected either to attend every class lecture or, in exceptional circumstances, to make arrangements with other students to obtain and study a copy of the lecture notes.  It is the student's responsibility to obtain the necessary exposure to the material presented in class. 
  


• Grading: The grade for the class will be based on performance in the exams. The grades will NOT be curved. I will set standards for the main changes in letter grade before grading the exams.  One intention of this grading scheme is that students compete against my standards in the course instead of against each other. I want to encourage students to work together and learn from each other.


• Ethics : The highest standards apply. In particular, instructions must be followed meticulously during exams to ensure equal conditions for all students.
  
  
• Religous or other conflicts with class activities: Send email or a note to Ian or drop by his office in the first two weeks of class if there is ANY chance of religious or other conflicts with any class activities that may be scheduled during the semester including any class time and the scheduled final exam.  Please specify the days or dates on which there is a potential or actual conflict. 

Text : Chen, Linear system theory and design, third edition, Oxford University Press 1998. ISBN 9780195117776
 

• Review of differential equations and linearization
• Review of vector spaces: vectors, independence, subspaces, maps (matrices), kernel, range, bases and coordinate changes
• Eigenvectors, eigenvalues, characteristic equation
• Diagonalization and semisimple matrices
• Engineering interpretation: modes
• Eigenvalues=poles in frequency domain


• Norms, matrix exponential
• Linear differential equation (time varying) and its solution
• Exponential of a semisimple matrix
• Complex eigenspaces and oscillations
• Jordan canonical form
• Cayley-Hamilton


• Controllability
• Observability
• Realizations


• BIBO stability
• Lyapunov and exponential stability


• Controllable canonical form
• State feedback and pole placement
• Stabilization
• Canonical decomposition
• McMillan degree
  

Possible additional topics as time permits:

• SISO compensator design and internal model principle
• Floquet theory for periodically time varying systems

Recommended ECE Control Courses after ECE717

• ECE409 Feedback Control Laboratory
• ECE417 Discrete Control
• ECE719 Optimal Sytems
  
• ECE720 Discrete Time Stochastic Systems
• ECE817 Nonlinear Systems
• ECE818 Linear Multivariable Systems
• ECE821 Optimal Control and Variational Methods
  

last updated 9 December 2008