**Description:**

Virtually all physical systems are nonlinear in nature. Sometimes, however, it is possible to describe the operation of a physical system by a linear model e.g., as a set of ordinary linear differential equations. This is the case, for example, if the mode of operation of the physical system does not deviate too much form the nominal set of operating conditions i.e., one can linearize the system. Thus the analysis of linear systems occupies an important place in system theory. But in analyzing the behavior of a physical system, one often encounters situations where the linear (or linearized) model is inadequate or inaccurate; that is the time when concepts from this course may prove useful.

The goal of the course is to address several main subjects in nonlinear control theory. We extend the notion of Lyapunov stability to systems with input i.e., input-to-state stability, show how Lyapunov stability is related to input-output stability and present/apply various nonlinear control design tools; passivity-based control, integral control, gain scheduling, Lyapunov redesign, sliding mode control, etc.

If time permits we will discuss controllability, observability and minimality of non-linear systems, elements of geometric control theory such as feedback linearization, etc., stabilization of control systems via discontinuous state feedback (sample-and-hold) and via continuous time-varying state feedback.

**Organizer:** Associate Professor John Leth, jjl@es.aau.dk

**Lecturer:** Associate Professor John Leth and Mihaly Petreczky, CNRS, Ecole
Centrale Lille, research group CIRStAL

**ECTS:** 2

**Time:** August 22-26, 2022

**Place:** TBA

**Number of seats:** 50

**Deadline:** August 1, 2022

**Important information concerning PhD courses:**

We have over some time experienced problems with no-show for both project and general courses. It has now reached a point where we are forced to take action. Therefore, the Doctoral School has decided to introduce a no-show fee of DKK 3.000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately four months before start. This can hopefully also provide new students a chance to register for courses during the year. We look forward to your registrations.

- Teacher: John-Josef Leth
- Teacher: Mihaly Petreczky