EE363: Linear Dynamical Systems
Next Taught 2008-09 (Not Offered 2007-08)
Lecture notes
- Linear quadratic regulator: Discrete-time
finite horizon (2up)
- LQR via Lagrange multipliers
(2up)
- Infinite horizon LQR (2up)
- Continuous-time LQR (2up)
- Invariant subspaces (2up)
- Estimation (2up)
- The Kalman filter (2up)
- The extended Kalman filter (2up)
- Conservation and dissipation
(2up)
- Basic Lyapunov theory (2up)
- Linear quadratic Lyapunov theory
(2up)
- Lyapunov theory with inputs and
outputs (2up)
- Linear matrix inequalities and the
S-procedure (2up)
- Analysis of systems with sector
nonlinearities (2up)
- Perron-Frobenius theory (2up)
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Support notes
Review session slides:
Support notes and exams:
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Homework
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Matlab files
Matlab files you'll need for homework assignments and exams.
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References
There is no textbook or reader; the lecture notes cover everything
you need. But if you'd like to look at some other texts covering
the same topics, we've listed some references below. More and more
good reference material is available online, and can be found using
google or wikipedia.
- A very good general reference that covers several of the topics
is Introduction to Dynamic Systems, Luenberger,
Wiley.
- LQR and Kalman filtering are covered in many books on linear
systems, optimal control, and optimization. One good one is
Dynamic Programming and Optimal Control, vol. 1,
Bertsekas, Athena Scientific. Another is Linear Optimal
Control, Anderson & Moore, Prentice-Hall.
- Lyapunov theory is covered in many texts on linear systems,
e.g., Linear Systems, Antsaklis & Michel,
McGraw-Hill. Nonlinear Lyapunov theory is covered in most texts on
nonlinear system analysis, e.g., Nonlinear systems: Analysis,
Stability, and Control, Sastry, Springer-Verlag, or
Nonlinear Systems Analysis (2nd edition), Vidyasagar,
SIAM.
- Lots of material on LMIs can be found in Boyd, El Ghaoui,
Feron, and Balakrishnan, Linear Matrix Inequalities
in System and Control Theory, but this is not a book for
casual browsing.
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Basic course info
Units: 3. Can be taken CR/NC. EE363 is in three EE depth
sequences: Control and System Engineering, Signal
Processing, and Dynamic Systems and Optimization.
Instructor: Stephen Boyd, Packard 264,
(650) 723-0002, boyd@stanford.edu.
Office hours: Tuesdays 10:45 - 12:30.
Administrative assistant: Denise Murphy, Packard 267,
(650) 723-4731, Fax (650) 723-8473, denise@ee.stanford.edu.
Lectures: Tuesdays and Thursdays 9:30-10:45 am, Gates
B03. Broadcast live by SCPD
on channel E2, and also available in streaming video format.
Problem session: Fridays 4:15-5:05 pm, Gates B03. The
problem session will be broadcast live by SCPD on channel E4, and available
online in streaming video format.
Teaching assistants:
TA office hours:
- Sundays (Packard 104) - 4:00-6:00 pm.
- Mondays (Packard 104) - 4:00-8:00 pm.
Catalog description: A continuation of EE263. Optimal control
and dynamic programming; linear quadratic regulator. Lyapunov
theory and methods. Time-varying and periodic systems. Realization
theory. Linear estimation and the Kalman filter. Examples and
applications from digital filters, circuits, signal processing, and
control systems.
Course requirements: weekly homework, take-home final
exam. These require some Matlab (or equivalent) programming.
Prerequisites: EE263 or equivalent, basic probability and
statistics as in Stat 116 or EE278.
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