# Lecture plan

## Lectures

For each lecture, one or two lecturers will be appointed. The lecturer has the responsibility of:

- Preparing a presentation of the literature for the given lecture.
- Preparing a number of questions for discussion during/after the presentation.
- Optional: Generating one or more exercises with solution, that illustrate and give an even better understanding of the material.
- E-mail the presentation material (and exercises) to Kristin Y. Pettersen for uploading to Blackboard by Monday morning before the lecture.

It is a main objective of the lectures to become trained in giving scientific lectures, and to have good discussions as these lead to a more thourough comprehension of the material. Although the lecturer have the responsibility of presenting the material, it is a joint responsibility for *all* attendants to prepare well by reading the literature in advance and participate actively in the discussions, preferably bringing their own questions for discussion.

## Schedule (Subject to changes)

Week | Dates | Topic | Literature | Lecturers | ||
---|---|---|---|---|---|---|

Syllabus | Background Material | |||||

3 | 16.01 | Introduction | Course information Reference group Level of detail | Lemma 3.4 Theorem 4.9 | Kristin Y. Pettersen | |

4 | 23.01 | Lyapunov stability | Converse theorems Boundedness and ultimate boundedness | Chapters 4.7 and 4.8 | Colloquium | |

5 | 30.01 | Input-Output Stability | L stability L stability of state models L _{2 } gain The small-gain theorem | Chapter 5 | Colloquium | |

6 | 06.02 | Stability of perturbed systems | Vanishing perturbation Nonvanishing perturbation Comparison method Continuity of solutions on the infinite interval Interconnected systems | Chapter 9.1 - 9.5 | Joakim R. Andersen | |

7 | 13.02 | Perturbation theory and averaging | The perturbation method Perturbation on the infinite interval Periodic perturbation of autonomous systems Averaging General averaging | Chapter 10 except 10.5 | Marianna Wrzos-Kaminska | |

9 | 27.02 | Frequency Domain Analysis of Feedback Systems | Absolute stability Circle criterion Popov criterion | Chapter 7.1 and relevant topics from Chapter 6 | Mishiga Vallabhan | |

10 | 06.03 | Feedback linearization | Full-state feedback linearization | Chapter 13 with a special emphasis on Ch. 13.3 and 13.4 | Isidori: Nonlinear Control Systems, Springer-Verlag, 3rd ed., 1995. Chapter 4 | Daniel Görner |

11 | 13.03 | Sliding mode control | Sliding mode control | Chapter 14.1 | Shtessel et al: Sliding mode control and observation, Birkhäuser Basel 2014 Chapter 1 and 4 L.Fridman: Sliding Mode Enforcement after 1990: Main Results and Some Open Problems, Springer 2011 | Marius Ulla Hatlehol |

12 | 20.03 | Backstepping | Backstepping | Chapter 14.3 | Krstic, Kanellakopoulos and Kokotovic: Nonlinear & Adaptive Control Design, Wiley 1995. Chapter 1-2 Adaptive backstepping: Chapter 3-4 | Dominik Zupan |

13 | 25-29.03 | Antonio Loria 5 days course | Stability Cascaded systems Matrosov´s theorem Lyapunov stability without Lyapunov functions | Handouts and selected papers | Antonio Loria |

**Literature:**

Hassan K. Khalil, *Nonlinear Systems*

Alternative 1: CU Nordics Edition, ISBN 9781784490133. The book can be bought at Akademika, Gløshaugen.

Alternative 2: 3rd Edition, Prentice Hall, 2002, 1995. ISBN 9780130673893. Click here to purchase the book at Amazon.com.

Both these editions contain the same material. The CU Nordics Edition is often less expensive than the 3rd edition.

(N.B.: Check the ISBN numbers to make sure that you get the correct edition. Several different editions exist, and for instance, the 2nd edition and the International edition does not contain all the material needed in this course. Also note that the book *Nonlinear Control* is a different book, and does not contain the material needed in this course.)

Selected conference and journal papers, in addition to handouts, in particular in connection with Antonio Loria´s lectures.