EECS221A
Linear System Theory

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

• Shankar Sastry
  717 Sutardja Dai Hall
  sastry at eecs.berkeley.edu
  Office hours: TBD

• Lillian Ratliff
  337 Cory Hall, Desk #11
  ratliffl at eecs.berkeley.edu
  Office hours: TBD
  

This course provides an introduction to the modern state space theory of linear systems for students of circuits, communications, controls and signal processing. In some sense it is a second course in linear systems, since it builds on an understanding that students have seen linear systems in use in at least some context before. The course is on the one hand quite classical and develops some rather well developed material, but on the other hand is quite modern and topical in that it provides a sense of the new vistas in embedded systems, computer vision, hybrid systems, distributed control, game theory and other current areas of strong research activity.

Topics include:

• A review of linear algebra and matrix theory. The solutions of linear equations.
• Least-squares approximation, linear programming, singular value decomposition and principal component analysis.
• Linear ordinary differential equations: existence and uniqueness of solutions, the state-transition matrix and matrix exponential.
• Numerical considerations: matrix sensitivity and condition number, numerical solutions to ordinary differential equations, and stiffness.
• 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, properties of the LQ regulator and Kalman filtering.
• Advanced topics such as robust control, hybrid system theory, linear quadratic games and distributed control will be presented based on allowable time and interest from the class.

It is recommended that students have previously taken a linear algebra course (MATH 110 or equivalent).

• 8/26 Course Outline

Announcements

Discussion

• Tutorial for Scientific Computing using Python
• Python Documentation
• Numpy and Scipy Documentation
• Richard Murray's Control Systems Library for Python
• Python-Control Toolbox Documentation
• Matplotlib (Python Plotting Tool)

• 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.
• D. F. Delchamps, State Space and Input-Output Linear Systems, Springer Verlag, 1988.

• 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.
• G. Strang, Introduction to Linear Algebra, 4th ed., Wellesley-Cambridge Press, 2009.

• J. Hale, Ordinary Differential Equations, Wiley.
• W. Rudin, Principles of Mathematical Analysis, Mcgraw-Hill.
• W. Rudin, Real and Complex Analysis, Mcgraw-Hill.
• B. Rynne and M.A. Youngson, Linear Functional Analysis, Springer, 2007.