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Nonlinear Control Systems

PhD course, Spring 2026


Lecturer and examiner:

Claudio Altafini, Automatic Control, ISY, Linköping University.


Aim

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.

Organization

10-12 lectures (2h each, once/twice a week), somewhere in the B-building, Campus Valla.

Schedule

  • L1. Wendnesday March 25 at 13:15-15 in Nollstället
  • L2. Wendnesday April 1 at 15:15-17 in Systemet
  • L3. Wendnesday April 8 at 15:15-17 in Transformen
  • L4. Wendnesday April 15 at 15:15-17 in Systemet
  • L5. Wendnesday April 22 at 15:15-17 in Systemet
  • L6. Wendnesday April 29 at 15:15-17 in Transformen
  • L7. Wendnesday May 6 at 15:15-17 in Systemet
  • HW1. Monday May 11 at 15:15-17 in Systemet
  • L8. Wendnesday May 13 at 15:15-17 in Systemet
  • L9. Wendnesday May 20 at 15:15-17 in Systemet
  • HW2. Monday May 25 at 15:15-17 in Nollstället
  • L10. Wendnesday May 27 at 15:15-17 in Systemet
  • L11. Wendnesday June 3 at 15:15-17 in Nollstället
  • HW3. Thursday June 18 at 10:15-12 in Systemet

Prerequisites

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

Topics

  • Lyapunov stability: Lyapunov direct method; La Salle invariance principle; Stability by linearization; stability of nonautonomous systems; converse theorems; center manifold.
  • Nonlinear controllability: differential geometric tools: manifolds, vector fields, Lie backets, Frobenius Theorem; controllablity and Chow Theorem; drift versus driftless systems, accessibility versus controllability; system inversion and differential flatness
  • Feedback linearization: state linearization; input-output feedback linearization; application to feedback stabilization, output tracking and disturbance decoupling.

Exam

Hand-in exercises during the course, plus (optional) final take home exam.

Credits: 6+3 p

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)
  • H. Nijmeijer, A. Van der Schaft. Nonlinear dynamical control systems. Springer, 1990.


Lecture notes which contain most of the material we will use are the following.

  • F. Ticozzi. Nonlinear Systems and Control, Lecture Notes, 2026.


My handwritten notes are also available.