UBC Home Page

-

UBC Home Page

-
UBC Home PageUBC Home Page-
-

-

-

Fall 2010

-EECE 571M
 

 

 

 

Home

Course Description and Content

 

Lecture Notes & ANNOUNCEMENTS

 

 

Useful links

 

ECE website

-


Nonlinear Systems and Control

Course Description

This graduate course covers fundamentals of nonlinear systems analysis and control. It is intended for studenst who have had a graduate course in linear dynamical systems, but no prior exposure to nonlinear dynamical systems. The first part of the course will focus on analysis of nonlinear systems, driven by a number of real-world examples, and some preliminary mathematical background. The second portion of the course will focus on stability through Lyapunov techniques and input-output analysis. The third portion of the course will focus on control of nonlinear systems, through feedback linearization, sliding mode control, and gain scheduling.

Course Outline and Syllabus

Course syllabus

  1. Introduction and review: Examples, linearization through Taylor's series.
  2. Analysis of nonlinear phenomena: Hartman-Grobmann theorem, local stability, multiple equilibria, limit cycles, bifurcations.
  3. Planar systems: phase plane techniques, Bendixson's theorem, Poincare-Bendixson Theorem.
  4. Mathematical background: Contraction mapping theorem, homeomorphisms, norms.
  5. Input-output analysis and stability: Small gain theorem, passivity, describing functions.
  6. Lyapunov stability theory: Lyapunov stability. Lyapunov functions, asymptotic stability, exponential stability, LaSalle's Theorem, Indirect method.
  7. Feedback linearization: Input-output linearization, full-state linearization, stabilization, tracking. Zero dynamics, MIMO systems, non-minimum phase systems, singularities.
  8. Sliding mode control: Sliding surfaces, differential inclusions, solutions in the sense of Filippov.
  9. Gain scheduling: Controller and scheduling design.

-



Last updated 1-Aug-2010

to top | UBC.ca » EECE 571M

EECE 571M Website
Electrical & Computer Engineering, KAIS building
tel (604) 822-2872 | fax (604) 822-5949 | e-mail webmaster[at]ece.ubc.ca

© Copyright The University of British Columbia, all rights reserved.