EE 500 : Linear System TheoryDepartment of Electrical and Systems Engineering University of Pennsylvania 

Fall 2003 
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 : Statetransition matrix, properties 
October 7  Lecture 10  Chapters 20, 21  Discretization of continuous systems, discretetime 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 