# Nonlinear Control Theory

**PhD course on Nonlinear Control, **(FRT025F)

#### Lecturer: Anders Robertsson, Bo Bernhardsson

The course is open for all PhD students and gives 7.5 ECTS credits.

#### Course description:

The goal of the course is to provide good knowledge and practice the

ability to use classical as well as modern analysis and design methods for

nonlinear control systems.

#### Contents:

Lyapunov theory for autonomous and time-varying systems,

Small-gain theory, Absolute stability, Integral quadratic constraints, Pas-

sivity, Center manifold theorem, Stability of periodic and perturbed sys-

tems, Averaging, Singular perturbations, Geometric control theory, Feed-

back linearization, Nonlinear design tools (backstepping, high gain con-

trol)

Language: Swedish or English

Literature:

H. K. Khalil, Nonlinear Systems 3rd ed. Prentice Hall, 2002,

ISBN 0-13-067389-7 + handout material [book home page with errata]

** **

- Mon April 23 13.15, Lecture notes 1 BoB
- Wed May 2, 15.15 Problem set 1 ARo (Seminar room M:2498)

- Tue May 8, 10.15 Lecture notes 2 BoB (Seminar room M:2498)
- Tue May 8, 15.15 (continue on Problem set 1) BoB (Seminar room M:2498)
- Tue May 15,
**8.15**ARo (Seminar room M:2498) (continued on Lecture notes 2 and some slides from Khalil lec #14,#15,#16, #17 ) - Tue May 15, Problem set 2, 15.15 BoB (Seminar room M:2498)
- Tue May 22, 10.15 Lecture notes 3 BoB (Seminar room M:2498)
- Tue May 22, 15.15 Lecture notes 4 BoB (Seminar room M:2498)
- Tue May 29, 10.15 Problem set 3 ARo
- Tue May 29, 15.15 ARo Slides from Khalil lec #22,#23 (Handout from T. Glad) and started on Lecture notes 6 (see below)
- Tue Jun 5, 10.15 ARo Lecture notes 6, The Joy of Feedback
- Tue Jun 5, 15.15 ARo (cont on Lec 6 notes)
- Mon Jun 11, 10.15 ARo Lecture notes 7, Inverse optimality, J-Q mm
- Tue Jun 19, 10.15 ARo2 b rescheduled
- Tue Jun 19, 15.15 ARo 2 b rescheduled
- Tue Jul 2, 08.15, BoB, Lecture notes 8, perturbation and averaging

Miniproject suggestions (2 persons each)

- Density functions: Alina and Christian
- Gröbner: Mahdi + NN? (sign up if interested)
- Flat systems: Björn and Ola

### Literature

H. K. Khalil, Nonlinear Systems 3rd ed. Prentice Hall, 2002,

ISBN 0-13-067389-7 [book home page with errata]

**Handout material:**

On the KYP-lemma by A. Rantzer

IQC_Lecture notes by U. Jönsson errata

IQC-paper by Megretski and Rantzer 1997

Seminar by Anton Shiriaev on Circle Criterion (version for 1st Swe-Chin conf.)

The Joy of Feedback (1991 Bode Prize Lecture by P. Kokotovic)

Old course home page (local access only)