## Time-Varying Systems and Computations

Module Number: EI5052

Duration: 1 Semester

Occurence: Winter Semester

Language: English

Number of ECTS: 6

## Staff

Professor in charge: Klaus Diepold

## Amount of Work

Contact hours: 90

Self-study hours: 90

Total: 180

## Description of Achievement and Assessment Methods

During an oral exam students proof taht they are able to extrapolate their abilitys acquired during the module to given problems.

The ability of team-oriented problem solving is assessed by problem-based homeworks (programming tasks) during the lecture period. For the assessment 4 work-sheets are handed out and graded.

Reading- and understanding competence as well as written communication skills are assesses with home-written essays. For the assessment 4 reading tasks are handed out for the students to answer questions and discuss.

Oral communication skills are assessed by a short presentation. Students present and explain topic-related and application-oriented literature to each other.

The final grade consists of:

exam: 50%

programming tasks: 30%

essays: 10%

presentation: 10%

## Prerequisites (recommended)

Working Knowledge of (numerical) Linearer Algebra, Linear Time-Invariant System Theory, Fundamentals of Signal Processing, Programming Skills in Matlab;

We expect students to have knowledge of material, which is taught in the following Bachelor courses at TUM:

- Signale, Systeme, Regelungstechnik, Lineare Algebra (1.Semester), Numerische Mathematik (4.Semester)

It is recommended to have particpated in the courses:

- Projektkurs Matlab (MSc)

- Numerical Methods of Electrical Engineering (MSc)

## Intended Learning Outcomes

After the course the student can create Matlab programs implementing efficient algorithms for solving large-scale and structured computational linear algebra problems for engineering applications. Students can analyse the effectiveness and efficiency of comutational linear algebra algorithms. The can analyse compuational engineering problems and express them in terms of linear time-varying systems concepts. Students can read and understand current research papers on the subject of efficient computations and explain their learnings to others in terms of oral and written communication.

## Content

Review of time-invariant systems and signals, Large scale computations in engineering and science, Computational problems involving Toeplitz matrices, Realization theory for LTI systems, Computational linear algebra and time-varying systems, State-space representation of LTV systems, Realization theory for LTV systems, Isometric and inner operators, inner-outer factorization, and operator inversion, Semi-seperable matrix structure. Mapping algorithms onto GPU architectures

## Teaching and Learning Methods

The course consists of a lecture given on a black board, which includes discussions of reading assignements (concept of inverted classroom; classical or current research papers on the subject), the exercises consists mainly of tipps, tricks and hints for the students to support them to accomplish their project tasks (programming), as well as answering specific questions asked by students, the exercises may also contain complementary presentations to selected mathematical topics, the students shall work in small teams (3-4 persons) in order to deliver about 5 project tasks throughout the semester, those project tasks will be problems that students need to write a program in Matlab to produce the requested results, the delivered solutions will be discussed with students to provide detailed feedback on their status. Students will also be asked to read literature, to produce correpsonding posters and present the content to all fellow students.

## Media

The following media types will be used:

- Frontal Presentation using Blackboard

- Guest Lecturers

- student presentations

- Write-up of lecture material (via download from Website),

- Literature reading assignments

- team-oriented programming tasks

- Matlab-Demos

## Reading List

The course will be based on material contained in the following books:

- P. Dewilde, A.-J. van der Veen. Time-Varying Systems and Computations. Kluwer Academic Publishers, 1998.

- G. Strang. Linear Algebra and its Applications. Hartcourt Brace Jovanovich Publishers, San Diego, 1988.

- G. Strang. Computational Science and Engineering. Wellesley-Cambridge Press, 2007.

- T. Kailath. Linear Systems. Prentice Hall, 1980.

- A.C. Antoulas. Approximation of Large-Scale Dynamical Systems. Advances in Design and Control. SIAM, Philadelphia, 2005.