*Course Syllabus for*
# Linear Systems

Linjära system

## FRT001F, 9 credits

**Valid from:** Autumn 2015

**Decided by:** it-tjo

**Date of establishment:** 2016-10-27

## General Information

**Division:** Automatic Control

**Course type:** Third-cycle course

**Teaching language:** English

## Aim

to learn fundamental theory for linear time-varying dynamical systems with several inputs and several outputs.

## Goals

*Knowledge and Understanding*

For a passing grade the doctoral student must

- understand how linear timevarying systems can be represented in different ways and how the relationships between the representations look like
- understand how controllability and observability can be analyzed with several different methods
- understand how realizations can be performed starting from transfer functions or Markov parameters
- be able to define and analyze various stability notions for linear timevarying systems
- be able to interpret least-squares problems in terms of linear operators and adjoint operators

*Competences and Skills*

For a passing grade the doctoral student must

- be able to linearize a timevarying system along a trajectory
- be able to determine Kalman's decomposition and a minimal realization of a system
- be able to verify exponential stability of a linear time-varying system using a Lyapunov function
- be able to determine the poles and zeros, including multiplicities, of a multivariable system

## Course Contents

Transition matrices. Controllability and observability. Realization theory. Stability theory. Operator theory. Multivariable input-output descriptions.

## Course Literature

Rugh, Wilson J.: Linear System Theory. Prentice Hall, 1996. ISBN 0134412052.

**Types of instruction:** Lectures, exercises

**Examination formats:** Written exam, written assignments

**Grading scale:** Failed, pass

**Examiner:**

## Admission Details

## Course Occasion Information

**Course coordinator:** Zhiyong Sun `<zhiyong.sun@control.lth.se>`