Announcements

  • No class on 10/30.

Topics

  • Norms, vector spaces, inner products
  • Bounded linear maps and stability
  • Fourier theory and the frequency domain
  • Toeplitz maps and convolution
  • Realization of state-space systems
  • Internal stability
  • Optimal control
  • Parametrization of all stabilizing controllers
  • Model reduction

Schedule

  • Class: Tu, Th, 4:15pm - 5:30pm, Room 540-108
  • Sanjay's office hours: Mon 3-5pm
  • Review session: Fri, 2-3pm, Durand 393
  • Laurent's Office hours: Mon, 1-3pm, Durand Computer Lab

Lecture Notes

  • 1. Vector Spaces and Norms (ps, pdf)
  • 2. The Peak-Induced Norm (ps, pdf)
  • 3. Convergence (ps, pdf)
  • 4. Fourier Series (ps, pdf)
  • 5. Toeplitz Operators (ps, pdf)
  • 6. Products and Inverses of Toeplitz Operators (ps, pdf)
  • 7. Spectral Factorization (ps, pdf)
  • 8. Smith-MacMillan Form (ps, pdf)
  • 9. Realization Theory (ps, pdf)
  • 10. Factorization (ps, pdf)

Homework

  • Homework 1 (ps, pdf)
  • Homework 1 solutions (ps, pdf)
  • Homework 2 (ps, pdf)
  • Homework 2 solutions (ps, pdf)
  • Homework 3 (ps, pdf)
  • Homework 3 solutions (ps, pdf)
  • Homework 4 (ps, pdf)
  • Homework 4 solutions (ps, pdf)
  • Homework 5 (ps, pdf)
  • Homework 5 solutions (ps, pdf)
  • Homework 6 (ps, pdf)
  • Homework 6 solutions (ps, pdf)
  • Homework 7 (ps, pdf)
  • Homework 7 solutions (ps, pdf)