Tentative Outline

• Abstract review of Linear System Theory

• Notes on Optimization, Linear Matrix Inequalities, Solvers and Parsers

• State feedback, Output feedback via LMIs

• Vector Spaces, Signal and System Norms, Interpretation of H2 and H∞ Norms

• H2 Control Problem

• Output Estimation Problem

• H∞ Control Problem

• Uncertainity Representations

• Linear Fractional Representations

• Robust Stability

• Structured Singular Value (µ-SSV)

• Computation of µ

• KYP Lemma

• Robust Performance

• Robust Control Synthesis

• Future Remarks

References:

• Class Notes

• LMIs in Control, C. Scherer and S. Weiland, Delft DCSC

• Linear Matrix Inequalities in Systems and Control theory, S. Boyd et.al, SIAM, 1994. (link)

• Yalmip, Sedumi

• A Course in Robust Control Theory: A Convex Approach, Springer, Dullerud, Paganini.

Software

• MATLAB Robust Control Toolbox, Yalmip

Evaluation

• 3-4 Homework assignments and 1 Final Homework.

 

 

Literature:

• Class Notes, Modern Control Theory, 3th Edt., W. Brogan, Prentice-Hall.
• Fundamentals of Linear State Space Systems, J.S. Bay, Mc-Graw Hill, 1999.

Grade Policy:

• 2 Midterm Exams (30%+30%)+ 1 Final Exam (40%)

  Aim of the course :

The course is intended to be a comprehensive treatment of the use of introductory level linear state space system theory in engineering problems. It is targeted at seniors of control branch although much of the material will be accessible to students with only basic signals and systems principles. The lecture uses the more natural and meaningful foundation of vector spaces and linear algebra. It is again inescapable that computer-aided engineering is an integral component of the lecture. Hence, the students are strongly encouraged to use MATLAB/SIMULINK in order to clarify the meaning of the material.

• Lecture 1 (Mathematical Modeling of Dynamical Systems, State-equation representation ) 1w

• Lecture 2 (Mathematical Foundation) 2w

• Lecture 3 (Transfer functions, Solution of state-equations, Computation of State-Transition Matrix) 1w

• Lecture 4 (Similarity Transformations, Eigenvalues and Eigenvectors, System modes, Realization) 1w

• Lecture 5 (Transmission zeros, Jordan Canonical Form) 2w

• Lecture 6 (Cayley-Hamilton Theorem and its applications) 1w

• Lecture 7 (Controllability, Observability, PBH tests, Introduction to State-feedback, Output-feedback) 1w

• Lecture 8 (State feedback control (Single-input, Multi-input cases)) 1w

• Lecture 9 (Observers, Full-Order Observer, Reduced-Order Observer Design, Obsever based control) 2w

 

Lecture Notes

Midterm

 

Midterm

Syllabus

1. introduction
2. Digital Systems and Binary numbers
3. Boolean Algebra and Logic Gates
4. Gate-level minimization
5. Combinational Logic
6. Synchronous Sequential Logic
7. Register and Counters
8. Asynchronous Sequential Logic

Book: There are many books on the subject but I prefer to use Mano, M. M., Digital Design, 4th Edt. Prentice Hall, 2007.

 

 

Course Outline

1. Mathematical Preliminaries
2. Linear State-Space Systems
3. Solution of State Equations
4. Existence and Uniqueness of Solutions
5. Computation of exp(At)
6. Solution of Periodic Systems
7. Internal Stability
8. Lyapunov Stability
9. Controllability
10. Observability
11. Standard Forms for Uncontrollable and Unobservable Syst.
12. PBH Test
13. Minimal Realization
14. Realization Techniques (Controller Form Realization, Observer Form Realization, Gilbert's Diagonal Realization)
15. Input-Output Stability
16. Linear Feedback
17. State and Output Feedback
18. Servomechanism Problem

References

1. Linear Systems, P.J. Antsaklis A.N. Michel
2. Linear Systems, Kailath
3. Linear System Theory, C. T. Chen
4. Matrix Analysis, R. A. Horn and C. R. Johnson