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Nonlinear Control Systems

PhD course, Spring 2017

Lecturer and examinator:

Claudio Altafini (ISY) claudio.altafini@liu.se


The course aims at giving an overview of the main control problems and of some of the mathematical tools required in the analysis and synthesis of nonlinear control systems.


12 lectures (2h each, once a week).

Schedule: Tuesdays at 13:15 in Algoritmen (B house, A-corridor). First class: March 7th.


Knowledge in Linear Algebra, Automatic Control, Linear System Theory (basic or advanced) is assumed.


Hand-in exercises during the course, plus final take home exam. Credits: 6+3 p

Topics (tentative):

  • Lyapunov stability
    • stability by linearization
    • Lyapunov theorems
    • La Salle invariance principle;
  • Nonlinear controllability
    • Differential geometric tools: manifolds, vector fields, Lie backets, Frobenius Theorem;
    • controllablity and Chow Theorem;
    • drift versus driftless systems, accessibility versus controllability;
  • Geometric methods for control synthesis
    • system inversion and differential flatness
    • feedback linearization;
  • Feedback stabilization
    • Brockett necessary condition
    • control Lyapunov functions

Course material:

There is no single book covering all material that will be treated in the course. Some parts can be found in the following:

  • H. Khalil. Nonlinear Systems, 3rd ed. Prentice Hall. 2002. (stability and stabilization)
  • Murray-Li-Sastry. A mathematical Introduction to Robotic Manipulation CRC press 1994. (Controllability; nonholonomic systems; Lie algebras)
  • F. Ticozzi. Nonlinear Systems and Control, Lecture Notes, 2016.
My handwritten notes are also available (thanks to Per)

Page responsible: Claudio Altafini
Last updated: 2017-05-23