University of California at Berkeley
Department of Electrical Engineering and Computer Sciences
EECS221A
Linear System Theory
Fall Semester 2007-2008
Course information:
UCB On-Line Course Catalog and Schedule of Classes
Lecture Information: TuTh 9.30-11, 247 Cory Hall.
Section Information: M 6-8pm, 400 Cory Hall.
Instructor
-
Professor Claire J. Tomlin,
259M Cory Hall
-
tomlin at eecs.berkeley.edu
-
http://www.eecs.berkeley.edu/~tomlin
-
Office hours: Tu 1-2pm, W 1-2pm
Teaching Assistant
-
Christophe Choumert,
Cory Hall
-
choumert at eecs.berkeley.edu
-
Office hours: Wednesday 5-7pm, Cory 382
Course Description
First graduate level course in linear systems theory. Review of linear algebra
and linear differential equations. Matrices and their eigenspaces.
Linear system representation for continuous and discrete time systems.
Stability. Controllability and observability. Realization theory.
Linear state feedback and estimation. Linear quadratic optimal control.
- Review of Linear Algebra: Rings, fields, vector spaces, matrices, bases, dimension of vector spaces,
properties of linear maps. Norms, induced norms.
- Differential Equations: Linear time-varying systems $\dot x = A(t) x(t) + B(t) u(t)$.
State transition matrix, properties of the state transition matrix. The adjoint equation.
The variational equation and its use in optimization. The linear time invariant case.
General system concepts and linearity.
- Difference equations: the discrete time system representation.
- Properties of the linear time invariant system representation:
Minimal polynomial, left and right eigenvectors, invariant subspaces,
direct sum of subspaces and the Jordan decomposition theorem. Functions
of a matrix, spectral mapping theorem. Numerical considerations: hermitian matrices,
adjoints, SVD, condition number.
- Stability: Input-output stability, internal stability for linear time-varying systems.
The linear time invariant case. Stability of discrete-time systems.
- Controllability and observability: Characterization, effects of feedback, output injection,
duality. Minimality and the Kalman decomposition, Realization, Hankel and Toeplitz matrices,
Controllable and observable canonical forms.
Stabilizability, detectability. The discrete-time case.
- Linear state feedback and estimation: controller design via linear state feedback,
design of full order and reduced order observers. The Separation Principle.
- Linear Quadratic Optimal Control: Least squares control and estimation, Riccati
equations and properties of the linear quadratic regulator (LQR).
- Unity Feedback systems: Robustness, transmission zeros, multiple-input multiple-output
Nyquist criterion.
Handouts
Homework
Announcements
- The midterm will be on Tuesday October 16 in class. One 8.5 by 11 crib sheet (both sides) is allowed.
- October 2, 4 classes will be taught by Alessandro Abate (aabate@eecs.berkeley.edu)
- September 13 class will be taught by Edgar Lobaton (lobaton@eecs.berkeley.edu)
Discussion
Fall 2006 discussions
Links
Mailing List
Please sign the handout sheet on the first day of lectures (Tues Aug 28), OR
email Professor Tomlin, so that your email will be added to the class mailing
list.
Grading
Homework 40%
Midterm 20%
Final 40%
Notes and Textbook
The course is based on a set of lecture notes which will be made available
throughout the term.
Recommended references are:
F.M. Callier and C.A. Desoer, Linear System Theory, Springer-Verlag, 1991.
T. Kailath, Linear Systems, Prentice-Hall, 1980.
Linear System Theory, by Wilson J. Rugh, 2nd Edition, Prentice
Hall, 1996
C.T. Chen, Linear Systems Theory and Design. Oxford University
Press, 3rd Edition, 1999
G. Strang, Linear Algebra and its Applications 3rd edition, 1988
(Linear Algebra Reference).
Updated 11/14/07