EE 500 : Linear Systems

	EE 500 : Linear System Theory Department of Electrical and Systems Engineering University of Pennsylvania
	Fall 2003

Announcements :
- First class is on Thursday September 4 in 212 Moore from 3:00-4:30pm.
Course Description: This graduate level course focuses on linear system theory in time domain. The course introduces the fundamental mathematics of linear spaces, linear operator theory,
and then proceeds with existence and uniqueness of solutions of differenial equations. Topics covered include
- Linear algebra review, solutions of linear differential equations, state space representations
- State transition matrix, time varying systems, the fundamental matrix.
- Structural properties of linear systems: controllability, observability and stability, realizations and minimality.
- Synthesis of linear controllers, pole placement, state feedback, observer design.
- Advance topics: Linear Quadratic Regulator theory, introduction to robust control.
Requirement: linear algebra, differential equations, and signals and systems (EE325 or equivalent). Undergraduates need permission.
Instructor:
- Ali Jadbabaie , jadbabai@seas.upenn.edu ,
  Office hours : Wednesdays 2:00-4:00pm, 365 GRW Moore bldg
Lectures: T- TR 3:00-4:30pm, Moore 212

Textbook
- Linear System Theory, by Wilson J. Rugh, 2nd Edition, Prentice Hall, 1996
Other References
- C.T. Chen, Linear Systems Theory and Design. Oxford University Press, 3rd Edition, 1999.

Grading :

Homeworks : 20%

Midterm I : 35%

Midterm II : 45%

Teaching assistants:

Nader Motee

Pranav Srivastava

Midterm I, due on Monday October 27 at 12:00pm.

Homeworks:

Homework 1: Problems 1.17, 2.1, 2.2, 2.3, 2.7, 2.8, 2.11. Due on Thursday September 18 in the class.

Homework 2: Problems 1, 8, 9, 10,11,12,13 from the first Linear Algebra handout . Due on Thursday September 25.

Homework 3: Problems 2, 3, 4, 5, 6, 7, from the same handout. Due on Thursday October 2.

Homework 4: Problems 5.1, 5.2, 5.3, 5.7, 5.8, 4.2, 4.10 From the textbook. Due on Thursday October 9th.

Homework 5: Problems 20.8, 20.9, 21.3, 21.5, 21.6, 6.3, 6.11 from the textbook. Due on Thursday October 16th

Homework 6: Problems 7.3, 7.4, 7.10, 7.11, 7.12, 7.15. Due on Thursday October 23.

Homework 7: Problems 9.1a, 9.2, 9.3, 9.4, 9.8, 9.13, 9.14, Due on Tuesday November 4 (Notice the extended deadlne).

Homework 8: Problems 9.1b, 9.5,9.10,9.15,13.5,13.11. Due on Thursday, November 6.

Homework 9: Problems 13.15, 13.16, 14.1, 14.2, 14.3, 14.4, 14.8. Due on Thursday November 13.

Homework 10: Problems 14.10, 15.1, 15.2, 15.5, 15.6, 15.9. Due on Thursday November 20.

Homework 11: Problems 12.2, 12.3,12.4, 12.12, 12.13, 12.14. Due on Monday December 2nd

A Tutorial on Linear Algebra by Professor C. T. Abdallah, University of New Mexico

Caution: There are some minor typos in the examples, see if you can find them!

Linear Algebra Review by Professor Fernando Paganini, UCLA.

Tentative Schedule (please note that the order might change):

Date Lecture Reading Contents

September 4 Lecture 1 Chapters 1, 2 Introduction, state space representations

September 9 Lecture 2 Chapter 2 State space representations

September 11 Lecture 3 Notes Linear algebra : Linear spaces, basis, norms, inner products

September 16 Lecture 4 Notes Linear algebra : Change of bases, y=Ax, eigenvalues, eigenvectors

September 18 Lecture 5 Notes Linear algebra : Diagonalization, Jordan forms

September 23 Lecture 6 Notes Linear algebra : more on Jordan forms, symmetric matrices

September 25 Lecture 7 Notes Functions of a square matrix, matrix exponential, Cayley Hamilton Theorem

September 30 Lecture 8 Chapters 4,5 State space solutions : Time Invariant and Time Varying cases, properties of the state transition matrix

October 2 Lecture 9 Chapters 4,5 State space solutions : State-transition matrix, properties

October 7 Lecture 10 Chapters 20, 21 Discretization of continuous systems, discrete-time state space solutions

October 9 Lecture 11 Chapter 6 Internal Stability: definitions

October 14 Lecture 12 Chapter 6 Uniform exponential stability and asymptotic stability. Time varying and Time Invariant cases

October 16 Lecture 13 Chapter 7 Lyapunov stability theorems: Time varying and time invariant cases

October 21 Lecture 14 Chapter 9 Controllability and Observability. Midterm 1

October 23 Lecture 15 Chapters 10,11, 13 more on controllability and observability: Kalman rank tests, PBH tests, decompositions

October 28 Lecture 16 Chapter 11 Observability : Kalman decomposition, minimal realizations, canonical forms

October 30 Lecture 17 Chapters 13,14 State feedback : Pole placement

November 4 Lecture 18 Chapter 15 More on pole placement

November 6 Lecture 19 Chapter 15 estimator design

November 11 Lecture 20 Chapter 15, Notes observers

November 13 Lecture 21 Notes reduced order observers/BIBO stability

November 19 Lecture 22 Notes BIBO stability/linear optimal control

November 20 Lecture 23 TBD TBD

November 25 Lecture 24 Linear Quadratic Regulator (LQR) Theory TBD

December 2 Lecture 25 TBD TBD, Midterm 2

December 4 Lecture 26 TBD TBD

Date	Lecture	Reading	Contents
September 4	Lecture 1	Chapters 1, 2	Introduction, state space representations
September 9	Lecture 2	Chapter 2	State space representations
September 11	Lecture 3	Notes	Linear algebra : Linear spaces, basis, norms, inner products
September 16	Lecture 4	Notes	Linear algebra : Change of bases, y=Ax, eigenvalues, eigenvectors
September 18	Lecture 5	Notes	Linear algebra : Diagonalization, Jordan forms
September 23	Lecture 6	Notes	Linear algebra : more on Jordan forms, symmetric matrices
September 25	Lecture 7	Notes	Functions of a square matrix, matrix exponential, Cayley Hamilton Theorem
September 30	Lecture 8	Chapters 4,5	State space solutions : Time Invariant and Time Varying cases, properties of the state transition matrix
October 2	Lecture 9	Chapters 4,5	State space solutions : State-transition matrix, properties
October 7	Lecture 10	Chapters 20, 21	Discretization of continuous systems, discrete-time state space solutions
October 9	Lecture 11	Chapter 6	Internal Stability: definitions
October 14	Lecture 12	Chapter 6	Uniform exponential stability and asymptotic stability. Time varying and Time Invariant cases
October 16	Lecture 13	Chapter 7	Lyapunov stability theorems: Time varying and time invariant cases
October 21	Lecture 14	Chapter 9	Controllability and Observability. Midterm 1
October 23	Lecture 15	Chapters 10,11, 13	more on controllability and observability: Kalman rank tests, PBH tests, decompositions
October 28	Lecture 16	Chapter 11	Observability : Kalman decomposition, minimal realizations, canonical forms
October 30	Lecture 17	Chapters 13,14	State feedback : Pole placement
November 4	Lecture 18	Chapter 15	More on pole placement
November 6	Lecture 19	Chapter 15	estimator design
November 11	Lecture 20	Chapter 15, Notes	observers
November 13	Lecture 21	Notes	reduced order observers/BIBO stability
November 19	Lecture 22	Notes	BIBO stability/linear optimal control
November 20	Lecture 23	TBD	TBD
November 25	Lecture 24	Linear Quadratic Regulator (LQR) Theory	TBD
December 2	Lecture 25	TBD	TBD, Midterm 2
December 4	Lecture 26	TBD	TBD

EE 500 : Linear System Theory