University of California at Berkeley
Department of Electrical Engineering and Computer Sciences
Linear System Theory
Fall Semester 2014
UCB On-Line Course Catalog and Schedule of Classes
Lecture Information: TuTh 2-3.30, 310 HMMB
Section Information: F 12-2, 241 Cory
721 Sutardja Dai Hall
tomlin at eecs.berkeley.edu
Office hours: Tuesday 11-12, Wednesday 10.30-11.30 (721 Sutardja Dai Hall)
balandat at eecs.berkeley.edu
Office hours: Monday 12:00-1:00, Wednesday 3:30-4:30 (337A Cory, inside the TRUST center)
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.
- 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).
Handouts and Lecture Notes
For information on the Section format see Course Outline
- Common math symbols: Link to Wikipedia Page
- The textbook Linear System Theory by Callier and Desoer can be found online through Springer. Link to C&D on Springer Website You must use Berkeley library credentials to access the book. Remotely, you may use a vpn service or a proxy. Instructions for VPN are located here. Instructions for setting up a proxy are located here.
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)
- Python Bootcamp and corresponding youtube video
- Prof. Claire Tomlin's video lectures on selected topics:
Introduction and Functions , Field and Vectors , Subspaces and Bases
Linear Maps , Matrix Representation of Linear Maps , Change of Basis
Norms , Induced Norms, Inner Products, Adjoints
Hermitian Matrices, Singular Value Decomposition
Fundamental Theorem of Ordinary Differential Equations, Bellman-Gronwall Lemma
Dynamical Systems, Linearity and Time invariance
Linear Time Varying Systems, State Transition Matrix, Solutions to Linear Time Varying Systems, Jacobian Linearization
The Matrix Exponetial
Cayley Hamilton Theorem
Homework 30%, there will be 10 problem sets
Midterm 30%, in class
- F. Callier & C. A. Desoer, Linear System Theory, 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.