Linear Systems (EE 60550)

University of Notre Dame

Fall 2011 -


Description: Simultaneous linear equations and orthogonal projections. Linear Algebra. State variable descriptions of linear dynamical systems. Solution of state equations for continuous-time and discrete-time systems. Input-output descriptions: impulse response and transfer function. Controllability, observability, canonical forms, stability. Realizations of input-output descriptions. State feedback and state observers. (Fall)

  1. Simultaneous Linear Equations and Linear Algebra Review
  2. System Representations and Linearization
  3. Causality, Time Invariance, and Linearity, Impulse Response and Transfer functions
  4. Solutions to LTV/LTI systems
  5. Lyapunov and Input-Output Stability
  6. LQR and Reachability (LTV)
  7. Reachability (LTI) and Controllable Decompositions
  8. Observability and Output Feedback
  9. Minimal Realizations and Matrix Fraction Descriptions

Grading: 20 % homework,40 % midterms, 40% final.
Instructor: Michael Lemmon, Fitz 264, Dept. of Electrical Engineering, University of Notre Dame, 631-8309 (lemmon at nd dot edu)
Textbooks:
  1. REQUIRED: J.P. Hespanha,, "Linear Systems Theory", Princeton University Press, 2009, (ISBN 978-0-691-14021-6)
  2. optional: G. Strang, " Linear Algebra and its Applications", 4th edition, Brooks-Cole, 2005, (ISBN 978-0-0301-0567-8)
  3. reference: P.J. Antsaklis and A.N. Michel, "Linear Systems", 2nd printing, Birkhauser, 2006.
  4. reference: T. Kailath, "Linear Systems", Prentice-Hall, 1980