EECS221A
Linear System Theory

Course information: UCB On-Line Course Catalog and Schedule of Classes

• Claire Tomlin
  721 Sutardja Dai Hall
  tomlin at eecs.berkeley.edu
  Office hours: Tu 3-4, W 11-12

• Christian Claudel
  claudel at eecs.berkeley.edu
  Office hours: M 4-5, W 9-10, 571 Cory

This course provides a comprehensive introduction to the modeling, analysis, and control of linear dynamical systems. Topics include: A review of linear algebra and matrix theory. The solutions of linear equations. Least-squares approximation and linear programming. Linear ordinary differential equations: existence and uniqueness of solutions, the state-transition matrix and matrix exponential. Input-output and internal stability; the method of Lyapunov. Controllability and observability; basic realization theory. Control and observer design: pole placement, state estimation. Linear quadratic optimal control: Riccati equation and properties of the LQ regulator. Advanced topics such as robust control and hybrid system theory will be presented based on allowable time and interest from the class.

This course provides a solid foundation for students doing research that requires the design and use of dynamic models. Students in control, circuits, signal processing, communications and networking are encouraged to take this course.

• Linear Algebra: Fields, vector spaces, subspaces, bases, dimension, range and Null spaces, linear operators, norms, inner products, adjoints.
• Matrix Theory: Eigenspaces, Jordan form, Hermitian forms, positive definiteness, singular value decomposition, functions of matrices, spectral mapping theorem, computational aspects.
• Optimization: Linear equations, least-squares approximation, linear programming.
• Differential Equations: existence and uniqueness of solutions, Lipschitz continuity, linear ordinary differential equations, the notion of state, the state-transition matrix.
• Stability: Internal stability, input-output stability, the method of Lyapunov.
• Linear Systems - open-loop aspects: controllability and observability, duality, canonical forms, the Kalman decomposition, realization theory, minimal realizations.
• Linear systems - feedback aspects: pole placement, stabilizability and detectability, observers, state estimation, the separation principle.
• Linear quadratic optimal control: least-squares control and estimation, Riccati equations, properties of the LQ regulator.
• Advanced topics: robust control, hybrid systems.

• 8/27 Course Outline
• 8/27 Lecture Notes 1
• 8/27 Lecture Notes 2
• 9/1 Lecture Notes 3
• 9/1 Lecture Notes 4
• 9/10 Lecture Notes 5
• 9/22 Lecture Notes 6
• 9/29 Lecture Notes 7
• 10/6 Lecture Notes 8
• 10/13 Lecture Notes 9
• 10/27 Lecture Notes 10
• 10/27 Lecture Notes 11
• 11/4 Lecture Notes 12
• 11/9 Lecture Notes 13
• 11/9 Lecture Notes 14
• 11/14 Lecture Notes 15
• 11/14 Lecture Notes 16

• 9/3 Homework 1 (due 9/15) . Solutions
• 9/15 Homework 2 (due 9/24) . Solutions
• 9/29 Homework 3 (due 10/8) . Solutions
• 10/8 Homework 4 (due 10/16) . Solutions
• 10/14 Midterm Review Problems
• 10/27 Homework 5 (due 11/5) . Solutions
• 11/6 Homework 6 (due 11/13) .
• 11/15 Homework 7 (due 11/24) .
• 11/24 Homework 8 (due 12/3) .

Announcements

Discussion

• 9/4 Section 1
• 9/11 Section 2
• 9/18 Section 3
• 9/25 Section 4
• 10/05 Section 5
• 10/09 Section 6
• 10/16 Section 7
• 10/30 Section 8
• 11/06 Section 9

• Online Controls Tutorial in MATLAB
• MATLAB Documentation Help Desk
• ODE Software for MATLAB (by Professor Polking at Rice University)

Please sign the handout sheet on the first day of lectures (Thurs Aug 27), OR email Tomlin, so that your email will be added to the class mailing list.

Homework 40%
Midterm 20%
Final 40%

There is no required text book. I will provide notes throughout the term, however I encourage you to take your own notes during lecture.

References

Systems:

• F. Callier & C. A. Desoer, Linear Systems, Springer-Verlag, 1991.
• C.T. Chen, Linear Systems Theory and Design, Holt, Rinehart & Winston, 1999.
• T. Kailath, Linear Systems Theory, Prentice-Hall.
• R. Brockett, Finite-dimensional Linear Systems, Wiley.
• W. J. Rugh, Linear System Theory, Prentice-Hall, 1996.

• G. Golub and C. Van Loan, Matrix Computations, Johns Hopkins Press.
• M. Gantmacher, Theory of Matrices, Vol 1 & 2, Chelsea.
• G. Strang, Linear Algebra and its Applications, 3rd edition, 1988.

• J. Hale, Ordinary Differential Equations, Wiley.
• W. Rudin, Principles of Mathematical Analysis, Mcgraw-Hill.
• W. Rudin, Real and Complex Analysis, Mcgraw-Hill.

Updated 8/24/09