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# Analysis and Control of Nonlinear Systems

## Module EI10004

This Module is offered by TUM Department of Electrical and Computer Engineering.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

### Basic Information

EI10004 is a module over more years in English language at Master’s level which is offered in winter semester.

This module description is valid from WS 2017/8 to SS 2018.

180 h 75 h 6 CP

### Content, Learning Outcome and Preconditions

#### Content

Fundamental Properties: existence and uniqueness of solutions, continuous dependencies on initial conditions and parameters, comparison principle; Lyapunov Stability: autonomous vs non-autonomous systems, comparison functions, converse Lyapunov theorems, boundedness and ultimate boundedness, input-to-state stability, incremental stability; Stability of Feedback Systems: passivity theorems, the small-gain theorems, absolute stability (circle and Popov criterion); Advanced Stability Analysis: center manifold theorems, region of attraction, invariance-like theorems; State Feedback Stabilization: feedback linearization, partial feedback linearization, passivity-based control, control Lyapunov functions.

#### Learning Outcome

After successful completion of the course, students are able to understand in depth the modeling of nonlinear control systems and the properties of their trajectories. They are able to rigorously analyze stability of nonlinear systems using Lyapunov functions and investigate their structural properties such as dissipativity. They can reason about stability of interconnected systems compositionally using the stability properties of the components. Finally, they are able to design continuous controllers enforcing some performance criterion on several classes of nonlinear control systems using partial feedback-linearization, passivity-based techniques, and control Lyapunov functions.

Control System 1

### Courses, Learning and Teaching Methods and Literature

#### Learning and Teaching Methods

Lecture is designed as an interactive session. The materials are covered step by step from scratch under the participation of the students. Several examples are exercised during each session with hand calculations on the blackboard so that students can deeply understand the covered materials.

#### Media

Black board
(Possibly) Lecture Notes

#### Literature

1. H. K. Khalil: Nonlinear Control, Prentice Hall, 2015.
2. J. J. Slotine and W. Li: Applied Nonlinear Control, Pearson, 1991.

### Module Exam

#### Description of exams and course work

The examination consists of a single written test at the end of the semester. The written examination is with closed book policy and no supporting material is allowed during the test. It consists of questions to determine the students' understanding of various concepts, e.g., Existence and Uniqueness of solutions, Comparison Principle, the Invariance Principle, Lyapunov Stability, Converse Lyapunov Theorems, InputtoState Stability, Incremental Stability, Passivity Theorems, SmallGain
Theorems, Backstepping, PassivityBased Control and so on. The final exam is a written one and its duration is 120 minutes.

#### Exam Repetition

There is a possibility to take the exam in the following semester.

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