Course Information

Linear System Theory - Spring 2011
Instructor: Prof. Songhwai Oh (오성회)
Email: songhwai (at) snu.ac.kr
Office Hours: MW 3:15-4:00PM
Office: Building 301 Room 702
Course Number: 4541.512

Time: TTh 2:00-3:15 PM
Location: Building 302 Room 408
TA: JungHun Suh (서정훈)
Email: weareperfect (at) snu.ac.kr
Office: Building 301 Room 718
 

Course Description


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, solutions of linear equations, matrix exponential, state transition matrix, input-output stability, internal stability, the method of Lyapunov, controllability and observability, realization theory, and state feedback and estimation.

Announcements


  • [05/25] The final exam will be held on June 15 (Wed) from 7PM to 9PM (Room 102, Building 301). This is a closed book exam.
  • [05/11] The due date for HW #3 is postponed to 5/16 (Monday).
  • [04/11] The midterm will be held on April 25 (Mon) April 20 (Wed) in class.  This is a closed book exam. The exam will cover materials up to the lecture on 4/13.
  • [04/08] HW2, problem 7 - It is the function "f" which satisfies the conditions of the fundamental theorem of differential equations.
  • [03/23] The last problem of homework #1 is updated to give a more precise algorithm.
  • [03/02] We will have the first lecture. Please review linear algebra before the class.
  • [03/01] Please read 배움의 윤리

Schedule


Week Reading Date Lecture Date Lecture
1       3/2
  • Introduction to Linear System Theory
2 Review linear algebra 3/7
  • Functions, field, ring
3/9
  • Vector spaces
  • Linear independence, basis, coordinates
3   3/14
  • Linear maps, matrix representation
  • Change of basis
3/16
  • Normed linear spaces, induced norms
  • Hilbert spaces, orthogonality
4   3/21
  • Adjoint
  • Projection theorem
3/23
  • Singular value decomposition
5 Chen Ch. 2 3/28
  • Fundamental theorem of
    differential equations
3/30
  • Dynamical system representation
  • Linear dynamical systems
6 Chen Ch. 4 4/4
  • State transition matrix
  • Adjoint equations
4/6
  • Linear quadratic (LQ) problem
7   4/11
  • Linear time invariant systems
  • Cayley-Hamilton theorem
4/13
  • State transition and response map
  • Eigenvector dyadic expansions
8   4/18
  • Basis of the solution space
4/20
  • Midterm
9   4/25
  • Second representation theorem
  • Minimal polynomial
4/27
  • Jordan decomposition theorem
  • Jordan form
10 Chen Ch. 5 5/2
  • Function of a matrix
  • Input-output stability
5/4
  • BIBO stability theorem
  • State space stability
11   5/9
  • Exponential stability
  • Connection to BIBO stability
5/11
  • Lyapunov stability
  • Stability of discrete-time systems
12 Chen Ch. 6 5/16
  • Controllability, observability
  • Controllability of (A(.),B(.))
5/18
  • Minimum cost control
  • Observability of (A(.),C(.))
13 Chen Ch. 7 5/23
  • Controllability of (A,B)
  • Observability of (A,C)
  • Kalman decomposition theorem
5/25
  • McMillan degree
  • Minimal realization theorem
14 Chen Ch. 8 5/30
  • State feedback
  • Eigenvalue assignment
6/1
  • State estimation
  • Separation property
15   6/6 -- 6/8  
16   6/13   6/15
  • Final exam (7-9 PM)
  • Room 102, Building 301

Textbooks


  • [Required] C.T. Chen, Linear Systems Theory and Design, Oxford University Press, 1999. (3rd Edition).
  • [Recommended] F. Callier and C. A. Desoer, Linear Systems, Springer-Verlag, 1991.
  • [Recommended] G. Strang, Linear Algebra and its Applications, 3rd edition, 1988.

Prerequisites


Students must have solid background in linear algebra and signals and systems.

Topics


  • Review of linear algebra and matrix theory
  • Norms and normed linear spaces, Inner product, Orthogonality, Projection theorem
  • Singular value decomposition
  • Solutions of linear ordinary differential equations
  • State space model, state transition matrix
  • Matrix exponential, Cayley-Hamilton theorem, Jordan form
  • Input-output stability, Internal stability
  • Lyapunov stability
  • Controllability, Observability
  • Kalman decomposition
  • Realization theory
  • State feedback and estimation
  • Advanced topics (if time permits)